Deck 11: Comparisons Involving Proportions and a Test of Independence

Question 1

Exhibit 11-2
Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.
$\begin{array}{ll}\text { Freshmen } & 83 \\\text { Sophomores } & 68 \\\text { Juniors } & 85 \\\text { Seniors } & 64\end{array}$ We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year.

-Refer to Exhibit 11-2. The expected number of freshmen is

A) 83
B) 90
C) 30
D) 10

Answer 1

90

Question 2

A population where each element of the population is assigned to one and only one of several classes or categories is a

A) multinomial population
B) Poisson population
C) normal population
D) None of these alternatives is correct.

Answer 2

A

Question 3

Exhibit 11-1
When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.
Do you support capital punishment?
$\begin{array}{lc}\begin{array}{l}\text { Do you support } \\\text { capital punishment? }\end{array} & \begin{array}{c}\text { Number of } \\\text { individuals }\end{array} \\\text { Yes } & 40 \\\text { No } & 60 \\\text { No Opinion } & 50\end{array}$ We are interested in determining whether or not the opinions of the individuals as to Yes, No, and No Opinion) are uniformly distributed.

-Refer to Exhibit 11-1. The number of degrees of freedom associated with this problem is

A) 150
B) 149
C) 2
D) 3

Answer 3

2

Question 4

A statistical test conducted to determine whether to reject or not reject a hypothesized probability distribution for a population is known as a

A) contingency test
B) probability test
C) goodness of fit test
D) None of these alternatives is correct.

Question 5

The degrees of freedom for a contingency table with 10 rows and 11 columns is

A) 100
B) 110
C) 21
D) 90

Question 6

If we are interested in testing whether the proportion of items in population 1 is larger than the proportion of items in population 2, the

A) null hypothesis should state P1 - P2 < 0
B) null hypothesis should state P1 - P2 > 0
C) alternative hypothesis should state P1 - P2 > 0
D) alternative hypothesis should state P1 - P2 < 0

Question 7

Exhibit 11-1
When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.
Do you support capital punishment?
$\begin{array}{lc}\begin{array}{l}\text { Do you support } \\\text { capital punishment? }\end{array} & \begin{array}{c}\text { Number of } \\\text { individuals }\end{array} \\\text { Yes } & 40 \\\text { No } & 60 \\\text { No Opinion } & 50\end{array}$ We are interested in determining whether or not the opinions of the individuals as to Yes, No, and No Opinion) are uniformly distributed.

-Refer to Exhibit 11-1. The conclusion of the test at 95% confidence) is that the

A) distribution is uniform
B) distribution is not uniform
C) test is inconclusive
D) None of these alternatives is correct.

Question 8

A goodness of fit test is always conducted as a

A) lower-tail test
B) upper-tail test
C) middle test
D) None of these alternatives is correct.

Question 9

In order not to violate the requirements necessary to use the chi-square distribution, each expected frequency in a goodness of fit test must be

A) at least 5
B) at least 10
C) no more than 5
D) less than 2

Question 10

The degrees of freedom for a contingency table with 6 rows and 3 columns is

A) 18
B) 15
C) 6
D) 10

Question 11

An important application of the chi-square distribution is

A) making inferences about a single population variance
B) testing for goodness of fit
C) testing for the independence of two variables
D) All of these alternatives are correct.

Question 12

Exhibit 11-1
When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.
Do you support capital punishment?
$\begin{array}{lc}\begin{array}{l}\text { Do you support } \\\text { capital punishment? }\end{array} & \begin{array}{c}\text { Number of } \\\text { individuals }\end{array} \\\text { Yes } & 40 \\\text { No } & 60 \\\text { No Opinion } & 50\end{array}$ We are interested in determining whether or not the opinions of the individuals as to Yes, No, and No Opinion) are uniformly distributed.

-Refer to Exhibit 11-1. The calculated value for the test statistic equals

A) 2
B) -2
C) 20
D) 4

Question 13

The sampling distribution of is approximated by a $\bar { p } _ { 1 } - \bar { p } _ { 2 }$

A) normal distribution
B) t-distribution with n1 + n2 degrees of freedom
C) t-distribution with n1 + n2 - 1 degrees of freedom
D) t-distribution with n1 + n2 + 2 degrees of freedom

Question 14

The sampling distribution for a goodness of fit test is the

A) Poisson distribution
B) t distribution
C) normal distribution
D) chi-square distribution

Question 15

Exhibit 11-1
When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.
Do you support capital punishment?
$\begin{array}{lc}\begin{array}{l}\text { Do you support } \\\text { capital punishment? }\end{array} & \begin{array}{c}\text { Number of } \\\text { individuals }\end{array} \\\text { Yes } & 40 \\\text { No } & 60 \\\text { No Opinion } & 50\end{array}$ We are interested in determining whether or not the opinions of the individuals as to Yes, No, and No Opinion) are uniformly distributed.

-Refer to Exhibit 11-1. The expected frequency for each group is

A) 0.333
B) 0.50
C) 1/3
D) 50

Question 16

The number of degrees of freedom for the appropriate chi-square distribution in a test of independence is

A) n-1
B) K-1
C) number of rows minus 1 times number of columns minus 1
D) a chi-square distribution is not used

Question 17

Exhibit 11-2
Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.
$\begin{array}{ll}\text { Freshmen } & 83 \\\text { Sophomores } & 68 \\\text { Juniors } & 85 \\\text { Seniors } & 64\end{array}$ We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year.

-Refer to Exhibit 11-2. The expected frequency of seniors is

A) 60
B) 20%
C) 68
D) 64

Question 18

Exhibit 11-1
When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained.
Do you support capital punishment?
$\begin{array}{lc}\begin{array}{l}\text { Do you support } \\\text { capital punishment? }\end{array} & \begin{array}{c}\text { Number of } \\\text { individuals }\end{array} \\\text { Yes } & 40 \\\text { No } & 60 \\\text { No Opinion } & 50\end{array}$ We are interested in determining whether or not the opinions of the individuals as to Yes, No, and No Opinion) are uniformly distributed.

-Refer to Exhibit 11-1. The p-value is

A) larger than 0.1
B) less than 0.1
C) less than 0.05
D) larger than 0.9

Question 19

Exhibit 11-2
Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.
$\begin{array}{ll}\text { Freshmen } & 83 \\\text { Sophomores } & 68 \\\text { Juniors } & 85 \\\text { Seniors } & 64\end{array}$ We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year.

-Refer to Exhibit 11-2. The calculated value for the test statistic equals

A) 0.5444
B) 300
C) 1.6615
D) 6.6615

Question 20

The degrees of freedom for a contingency table with 12 rows and 12 columns is

A) 144
B) 121
C) 12
D) 120

Question 21

Exhibit 11-2
Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.
$\begin{array}{ll}\text { Freshmen } & 83 \\\text { Sophomores } & 68 \\\text { Juniors } & 85 \\\text { Seniors } & 64\end{array}$ We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year.

-Refer to Exhibit 11-2. The p-value is

A) less than .005
B) between .025 and 0.05
C) between .05 and 0.1
D) greater than 0.1

Question 22

Exhibit 11-6
The following shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.
$\begin{array}{lc}\text { Political Party }&\text { Support }\\\text { Democrats } & 100 \\\text { Republicans } & 120 \\\text { Independents } & 80\end{array}$ We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed.

-Refer to Exhibit 11-6. The calculated value for the test statistic equals

A) 300
B) 4
C) 0
D) 8

Question 23

Exhibit 11-2
Last school year, the student body of a local university consisted of 30% freshmen, 24% sophomores, 26% juniors, and 20% seniors. A sample of 300 students taken from this year's student body showed the following number of students in each classification.
$\begin{array}{ll}\text { Freshmen } & 83 \\\text { Sophomores } & 68 \\\text { Juniors } & 85 \\\text { Seniors } & 64\end{array}$ We are interested in determining whether or not there has been a significant change in the classifications between the last school year and this school year.

-Refer to Exhibit 11-2. At 95% confidence, the null hypothesis

A) should not be rejected
B) should be rejected
C) was designed wrong
D) None of these alternatives is correct.

Question 24

Exhibit 11-3
In order to determine whether or not a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below.
$\begin{array}{lll}&\text { Patients Cured }&\text { Patients Not Cured }\\\text { Received medication } & 70 & 10 \\\text { Received sugar pills } & 20 & 50\end{array}$ We are interested in determining whether or not the medication was effective in curing the common cold.

-Refer to Exhibit 11-3. The expected frequency of those who received medication and were cured is

A) 70
B) 150
C) 28
D) 48

Question 25

Exhibit 11-5
The table below gives beverage preferences for random samples of teens and adults.
$\begin{array}{lrrr}&\text { Teens}&\text { Adults }&\text {Total }\\\text { Coffee } & 50 & 200 & 250 \\\text { Tea } & 100 & 150 & 250 \\\text { Soft Drink } & 200 & 200 & 400 \\\text { Other } & 50 & 50 & 100\\400&400&600&1,000\end{array}$ We are asked to test for independence between age i.e., adult and teen) and drink preferences.

-Refer to Exhibit 11-5. With a .05 level of significance, the critical value for the test is

A) 1.645
B) 7.815
C) 14.067
D) 15.507

Question 26

Exhibit 11-3
In order to determine whether or not a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below.
$\begin{array}{lll}&\text { Patients Cured }&\text { Patients Not Cured }\\\text { Received medication } & 70 & 10 \\\text { Received sugar pills } & 20 & 50\end{array}$ We are interested in determining whether or not the medication was effective in curing the common cold.

-Refer to Exhibit 11-3. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals

A) 3.84
B) 7.81
C) 5.99
D) 9.34

Question 27

Exhibit 11-4
In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College.
Refer to Exhibit 11-4. The p-value is

A) greater than 0.1
B) between 0.05 and 0.1
C) between 0.025 and 0.05
D) between 0.01 and .025

Question 28

Exhibit 11-4
In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College.
Refer to Exhibit 11-4. The expected frequency for the Business College is

A) 0.3
B) 0.35
C) 90
D) 105

Question 29

Exhibit 11-3
In order to determine whether or not a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below.
$\begin{array}{lll}&\text { Patients Cured }&\text { Patients Not Cured }\\\text { Received medication } & 70 & 10 \\\text { Received sugar pills } & 20 & 50\end{array}$ We are interested in determining whether or not the medication was effective in curing the common cold.

-Refer to Exhibit 11-3. The number of degrees of freedom associated with this problem is

A) 4
B) 149
C) 1
D) 3

Question 30

Exhibit 11-5
The table below gives beverage preferences for random samples of teens and adults.
$\begin{array}{lrrr}&\text { Teens}&\text { Adults }&\text {Total }\\\text { Coffee } & 50 & 200 & 250 \\\text { Tea } & 100 & 150 & 250 \\\text { Soft Drink } & 200 & 200 & 400 \\\text { Other } & 50 & 50 & 100\\400&400&600&1,000\end{array}$ We are asked to test for independence between age i.e., adult and teen) and drink preferences.

-Refer to Exhibit 11-5. The test statistic for this test of independence is

A) 0
B) 8.4
C) 62.5
D) 82.5

Question 31

Exhibit 11-6
The following shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.
$\begin{array}{lc}\text { Political Party }&\text { Support }\\\text { Democrats } & 100 \\\text { Republicans } & 120 \\\text { Independents } & 80\end{array}$ We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed.

-Refer to Exhibit 11-6. The expected frequency for each group is

A) 0.333
B) 0.50
C) 50
D) None of these alternatives is correct.

Question 32

Exhibit 11-4
In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College.
Refer to Exhibit 11-4. This problem is an example of a

A) normally distributed variable
B) test for independence
C) Poisson distributed variable
D) multinomial population

Question 33

Exhibit 11-3
In order to determine whether or not a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below.
$\begin{array}{lll}&\text { Patients Cured }&\text { Patients Not Cured }\\\text { Received medication } & 70 & 10 \\\text { Received sugar pills } & 20 & 50\end{array}$ We are interested in determining whether or not the medication was effective in curing the common cold.

-Refer to Exhibit 11-3. The p-value is

A) less than .005
B) between .005 and .01
C) between .01 and .025
D) between .025 and .05

Question 34

Exhibit 11-4
In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College.
Refer to Exhibit 11-4. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals

A) 1.645
B) 1.96
C) 5.991
D) 7.815

Question 35

Exhibit 11-4
In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College.
Refer to Exhibit 11-4. The conclusion of the test is that the

A) proportions have changed significantly
B) proportions have not changed significantly
C) test is inconclusive
D) None of these alternatives is correct.

Question 36

Exhibit 11-5
The table below gives beverage preferences for random samples of teens and adults.
$\begin{array}{lrrr}&\text { Teens}&\text { Adults }&\text {Total }\\\text { Coffee } & 50 & 200 & 250 \\\text { Tea } & 100 & 150 & 250 \\\text { Soft Drink } & 200 & 200 & 400 \\\text { Other } & 50 & 50 & 100\\400&400&600&1,000\end{array}$ We are asked to test for independence between age i.e., adult and teen) and drink preferences.

-Refer to Exhibit 11-5. The expected number of adults who prefer coffee is

A) 0.25
B) 0.33
C) 150
D) 200

Question 37

Exhibit 11-4
In the past, 35% of the students at ABC University were in the Business College, 35% of the students were in the Liberal Arts College, and 30% of the students were in the Education College. To see whether or not the proportions have changed, a sample of 300 students was taken. Ninety of the sample students are in the Business College, 120 are in the Liberal Arts College, and 90 are in the Education College.
Refer to Exhibit 11-4. The calculated value for the test statistic equals

A) 0.01
B) 0.75
C) 4.29
D) 4.38

Question 38

Exhibit 11-3
In order to determine whether or not a particular medication was effective in curing the common cold, one group of patients was given the medication, while another group received sugar pills. The results of the study are shown below.
$\begin{array}{lll}&\text { Patients Cured }&\text { Patients Not Cured }\\\text { Received medication } & 70 & 10 \\\text { Received sugar pills } & 20 & 50\end{array}$ We are interested in determining whether or not the medication was effective in curing the common cold.

-Refer to Exhibit 11-3. The test statistic is

A) 10.08
B) 54.02
C) 1.96
D) 1.645

Question 39

Exhibit 11-6
The following shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.
$\begin{array}{lc}\text { Political Party }&\text { Support }\\\text { Democrats } & 100 \\\text { Republicans } & 120 \\\text { Independents } & 80\end{array}$ We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed.

-Refer to Exhibit 11-6. The number of degrees of freedom associated with this problem is

A) 2
B) 3
C) 300
D) 299

Question 40

Exhibit 11-5
The table below gives beverage preferences for random samples of teens and adults.
$\begin{array}{lrrr}&\text { Teens}&\text { Adults }&\text {Total }\\\text { Coffee } & 50 & 200 & 250 \\\text { Tea } & 100 & 150 & 250 \\\text { Soft Drink } & 200 & 200 & 400 \\\text { Other } & 50 & 50 & 100\\400&400&600&1,000\end{array}$ We are asked to test for independence between age i.e., adult and teen) and drink preferences.

-Refer to Exhibit 11-5. The p-value is

A) between .1 and .05
B) between .05 and .025
C) between .025 and .01
D) less than 0.005

Question 41

Exhibit 11-7
The results of a recent poll on the preference of shoppers regarding two products are shown below.
$$\begin{array}{l}&&\text { Shoppers Favoring }\\\text { Product } & \text { Shoppers Surveyed } & \text { This Product } \\\text { A } & 800 & 560 \\\text { B } & 900 & 612\end{array}$$

-Refer to Exhibit 11-7. The 95% confidence interval estimate for the difference between the populations favoring the products is

A) -0.024 to 0.064
B) 0.6 to 0.7
C) 0.024 to 0.7
D) 0.02 to 0.3

Question 42

Exhibit 11-9
The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below.
$$\begin{array} { l c c } &&\text { Teenagers Favoring }\\\text { Music Type } & \text { Teenagers Surveyed } & \text { This Type } \\\text { Pop } & 800 &384 \\\text { Rap } & 900 & 450\\\end{array}$$

-Refer to Exhibit 11-9. The 95% confidence interval for the difference between the two proportions is

A) 384 to 450
B) 0.48 to 0.5
C) 0.028 to 0.068
D) -0.068 to 0.028

Question 43

Exhibit 11-8
An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below.
$\begin{array}{ll}\text { Under Age of 18}&\text { Over Age of 18}\\\mathrm{n}_{1}=500 & \mathrm{n}_{2}=600 \\\text { Number of accidents }=180 & \text { Number of accidents }=150\end{array}$
We are interested in determining if the accident proportions differ between the two age groups.

-Refer to Exhibit 11-8. The test statistic is

A) 0.96
B) 1.96
C) 2.96
D) 3.96

Question 44

Among a sample of 50 M.D.'s medical doctors) in the city of Memphis, Tennessee, 10 indicated they make house calls; while among a sample of 100 M.D.'s in Atlanta, Georgia, 18 said they make house calls. Determine a 95% interval estimate for the difference between the proportion of doctors who make house calls in the two cities.

Question 45

A comparative study of organic and conventionally grown produce was checked for the presence of E. coli. Results are summarized below. Is there a significant difference in the proportion of E. Coli in organic vs. conventionally grown produce? Test at ? = 0.10.
$\begin{array}{llc}&\text {Sample Size}&\text {E. Coli Prevalence}\\\text { Organic } & 200 & 3 \\\text { Connentional } & 500 & 20\end{array}$

Question 46

Of 200 UTC seniors surveyed, 60 were planning on attending Graduate School. At UTK, 400 seniors were surveyed and 100 indicated that they were planning to attend Graduate School.
a. Determine a 95% confidence interval estimate for the difference between the proportion of seniors at the two universities that were planning to attend Graduate School.
b. Is there conclusive evidence to prove that the proportion of students from UTC who plan to go to Graduate School is significantly more than those from UTK? Explain.

Question 47

Of 300 female registered voters surveyed, 120 indicated they were planning to vote for the incumbent president; while of 400 male registered voters, 140 indicated they were planning to vote for the incumbent president.
a. Compute the test statistic.
b. At alpha = .05, test to see if there is a significant difference between the proportions of females and males who plan to vote for the incumbent president. Use the p-value approach.)

Question 48

Exhibit 11-8
An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below.
$\begin{array}{ll}\text { Under Age of 18}&\text { Over Age of 18}\\\mathrm{n}_{1}=500 & \mathrm{n}_{2}=600 \\\text { Number of accidents }=180 & \text { Number of accidents }=150\end{array}$
We are interested in determining if the accident proportions differ between the two age groups.

-Refer to Exhibit 11-8. The pooled proportion is

A) 0.305
B) 0.300
C) 0.027
D) 0.450

Question 49

Exhibit 11-9
The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below.
$$\begin{array} { l c c } &&\text { Teenagers Favoring }\\\text { Music Type } & \text { Teenagers Surveyed } & \text { This Type } \\\text { Pop } & 800 &384 \\\text { Rap } & 900 & 450\\\end{array}$$

-We are interested in testing the following hypotheses. H0: P1- P2 = 0 Ha: P1- P2 ? 0
The test statistic Z is computed to be 2.0. The p-value for this test is

A) 0.9772
B) 1.9544
C) 0.0228
D) 0.0456

Question 50

Exhibit 11-8
An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below.
$\begin{array}{ll}\text { Under Age of 18}&\text { Over Age of 18}\\\mathrm{n}_{1}=500 & \mathrm{n}_{2}=600 \\\text { Number of accidents }=180 & \text { Number of accidents }=150\end{array}$
We are interested in determining if the accident proportions differ between the two age groups.

-Refer to Exhibit 11-8 and let pu represent the proportion under and po the proportion over the age of 18. The null hypothesis is

A) pu - po ? 0.
B) pu - po ? 0 .
C) pu - po ? 0
D) pu - po = 0

Question 51

Exhibit 11-7
The results of a recent poll on the preference of shoppers regarding two products are shown below.
$$\begin{array}{l}&&\text { Shoppers Favoring }\\\text { Product } & \text { Shoppers Surveyed } & \text { This Product } \\\text { A } & 800 & 560 \\\text { B } & 900 & 612\end{array}$$

-Refer to Exhibit 11-7. At 95% confidence, the margin of error is

A) 0.064
B) 0.044
C) 0.0225
D) 52

Question 52

Exhibit 11-8
An insurance company selected samples of clients under 18 years of age and over 18 and recorded the number of accidents they had in the previous year. The results are shown below.
$\begin{array}{ll}\text { Under Age of 18}&\text { Over Age of 18}\\\mathrm{n}_{1}=500 & \mathrm{n}_{2}=600 \\\text { Number of accidents }=180 & \text { Number of accidents }=150\end{array}$
We are interested in determining if the accident proportions differ between the two age groups.

-Refer to Exhibit 11-8. The p-value is

A) less than 0.001
B) more than 0.10
C) 0.0228
D) 0.3

Question 53

During the primary elections of 1996, candidate A showed the following pre-election voter support in Tennessee and Mississippi.
Voters Surveyed Voters Favoring Candidate A
Tennessee 500 295
Mississippi 700 357
a. Develop a 95% confidence interval estimate for the difference between the proportion of voters favoring candidate A in the two states.
b. Is there conclusive evidence that one of the two states had a larger proportion of voters' support? If yes, which state? Explain.

Question 54

Exhibit 11-9
The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below.
$$\begin{array} { l c c } &&\text { Teenagers Favoring }\\\text { Music Type } & \text { Teenagers Surveyed } & \text { This Type } \\\text { Pop } & 800 &384 \\\text { Rap } & 900 & 450\\\end{array}$$

-For a one-tailed test lower tail) at 99.7% confidence, Z =

A) ± 1.86
B) - 2.75
C) ±1.96
D) -1.645

Question 55

Of 150 Chattanooga residents surveyed, 60 indicated that they participated in a recycling program. In Knoxville, 120 residents were surveyed and 36 claimed to recycle.
a. Determine a 95% confidence interval estimate for the difference between the proportion of residents recycling in the two cities.
b. From your answer in Part a, is there sufficient evidence to conclude that there is a significant difference in the proportion of residents participating in a recycling program?

Question 56

Exhibit 11-9
The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below.
$$\begin{array} { l c c } &&\text { Teenagers Favoring }\\\text { Music Type } & \text { Teenagers Surveyed } & \text { This Type } \\\text { Pop } & 800 &384 \\\text { Rap } & 900 & 450\\\end{array}$$

-For a two-tailed test at 98.5% confidence, Z =

A) ± 2.17
B) ± 1.96
C) ± 2.98
D) ± 2.43

Question 57

Exhibit 11-9
The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below.
$$\begin{array} { l c c } &&\text { Teenagers Favoring }\\\text { Music Type } & \text { Teenagers Surveyed } & \text { This Type } \\\text { Pop } & 800 &384 \\\text { Rap } & 900 & 450\\\end{array}$$

-We are interested in testing the following hypotheses. H0: P1- P2 ? 0
Ha: P1- P2 > 0
The test statistic Z is computed to be 0.58. The p-value for this test is

A) 0.7190
B) 0.2810
C) 0.5620
D) 0.5800

Question 58

Exhibit 11-7
The results of a recent poll on the preference of shoppers regarding two products are shown below.
$$\begin{array}{l}&&\text { Shoppers Favoring }\\\text { Product } & \text { Shoppers Surveyed } & \text { This Product } \\\text { A } & 800 & 560 \\\text { B } & 900 & 612\end{array}$$

-Refer to Exhibit 11-7. The point estimate for the difference between the two population proportions in favor of this product is

A) 52
B) 100
C) 0.44
D) 0.02

Question 59

Exhibit 11-9
The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below.
$$\begin{array} { l c c } &&\text { Teenagers Favoring }\\\text { Music Type } & \text { Teenagers Surveyed } & \text { This Type } \\\text { Pop } & 800 &384 \\\text { Rap } & 900 & 450\\\end{array}$$

-Refer to Exhibit 11-9. The standard error of is

A) 0.48
B) 0.50
C) 0.03
D) 0.0243

Question 60

Exhibit 11-9
The results of a recent poll on the preference of teenagers regarding the types of music they listen to are shown below.
$$\begin{array} { l c c } &&\text { Teenagers Favoring }\\\text { Music Type } & \text { Teenagers Surveyed } & \text { This Type } \\\text { Pop } & 800 &384 \\\text { Rap } & 900 & 450\\\end{array}$$

-Refer to Exhibit 11-9. The point estimate for the difference between the proportions is

A) -0.02
B) 0.048
C) 100
D) 66

Question 61

The results of a recent poll on the preference of voters regarding presidential candidates are shown below.
Candidate
Voters Surveyed
Voters Favoring This Candidate
A 400 192
B 450 225
At 95% confidence, test to determine whether or not there is a significant difference between the preferences for the two candidates.

Question 62

A poll was taken this year asking college students if they considered themselves overweight. A similar poll was taken five years ago. Results are summarized below. Has the proportion increased significantly? Let α = 0.05.
Sample Size Number Considered
Themselves Overweight
Present Sample 300 150
Previous sample 275 121

Question 63

In a sample of 100 Republicans, 60 favored the President's anti-drug program. While in a sample of 150 Democrats, 84 favored his program. At 95% confidence, test to see if there is a significant difference in the proportions of the Democrats and the Republicans who favored the President's anti-drug program.

Question 64

During the recent primary elections, the democratic presidential candidate showed the following pre-election voter support in Alabama and Mississippi.
State Voters Surveyed
Voters Favoring the Democratic Candidate
Alabama 800 440
Mississippi 600 360
a. We want to determine whether or not the proportions of voters favoring the Democratic candidate were the same in both states. Provide the hypotheses.
b. Compute the test statistic.
c. Determine the p-value; and at 95% confidence, test the above hypotheses.

Question 65

A medical journal reported the following frequencies of deaths due to cardiac arrest for each day of the week:
Cardiac Death by Day of the Week
We want to determine whether the number of deaths is uniform over the week.
a. Compute the test statistic.
b. Using the p-value approach at 95% confidence, test for the uniformity of death over the week.
c. Using the critical value approach, perform the test for uniformity.

Question 66

In 2013, forty percent of the students at a major university were Business majors, 35% were Engineering majors and the rest of the students were majoring in other fields. In a sample of 600 students from the same university taken in 2014, two hundred were Business majors, 220 were Engineering majors and the remaining students in the sample were majoring in other fields. At 95% confidence, test to see if there has been a significant change in the proportions between 2013 and 2014.

Question 67

The results of a recent poll on the preference of voters regarding the presidential candidates are shown below.
Voters Surveyed
Voters Favoring This Candidate
Candidate A 200 150
Candidate B 300 195
a. Develop a 90% confidence interval estimate for the difference between the proportion of voters favoring each candidate.
b. Does your confidence interval provide conclusive evidence that one of the candidates is favored more? Explain.

Question 68

Babies weighing less than 5.5 pounds at birth are considered "low­birth­weight babies." In the United States, 7.6% of newborns are low-birth-weight babies. The following information was accumulated from samples of new births taken from two counties.
$\begin{array}{lcc}&\text { Hamilton }&\text { Shelby }\\\text { Sample size } & 150 & 200 \\\text { Number of "low-birth-weight babies } & 18 & 22\end{array}$

a. Develop a 95% confidence interval estimate for the difference between the proportions of low-birth-weight babies in the two counties.
b. Is there conclusive evidence that one of the proportions is significantly more than the other? If yes, which county? Explain, using the results of part a). Do not perform any test.

Question 69

Among 1,000 managers with degrees in business administration, the following data have been accumulated as to their fields of concentration.
$\begin{array}{lrrr}\text {Major}&\text {Top Management}&\text { Middle Management}&\text {TOTAL}\\\text { Management } & 280 & 220 & 500 \\\text { Marketing } & 120 & 80 & 200 \\\text { Accounting } & 150 & 150 & 300 \\\text { TOTAI } & \mathbf{500} & \mathbf{4 5 0} & \mathbf{1000}\end{array}$
We want to determine if the position in management is independent of field major) of concentration.
a. Compute the test statistic.
b. Using the p-value approach at 90% confidence, test to determine if management position is independent of major.
c. Using the critical value approach, test the hypotheses. Let ? = 0.10.

Question 70

Before the start of the Winter Olympics, it was expected that the percentages of medals awarded to the top contenders to be as follows.
Midway through the Olympics, of the 120 medals awarded, the following distribution was observed.
We want to test to see if there is a significant difference between the expected and actual awards given.
a. Compute the test statistic.
b. Using the p-value approach, test to see if there is a significant difference between the expected and the actual values. Let α = .05.
c. At 95% confidence, test for a significant difference using the critical value approach.

Question 71

From a poll of 800 television viewers, the following data have been accumulated as to their levels of education and their preference of television stations. We are interested in determining if the selection of a TV station is independent of the level of education.
Educational Level

$\begin{array}{rrrrr}&\text { High School } & \text { Bachelor } &\text { Graduate }& \text { TOTAL }\\\text { Public Broadcasting } & 50 & 150 & 80 & 280 \\\text { Commercial Stations } & 150 & 250 & 120 & 520\\\text { TOTAL } & 200 & 400 & 200 & 800\end{array}$
a. State the null and the alternative hypotheses.
b. Show the contingency table of the expected frequencies.
c. Compute the test statistic.
d. The null hypothesis is to be tested at 95% confidence. Determine the critical value for this test.
e. Determine the p-value and perform the test.

Question 72

Before the presidential debates, it was expected that the percentages of registered voters in favor of various candidates would be as follows.
After the presidential debates, a random sample of 1200 voters showed that 540 favored the Democratic candidate; 480 were in favor of the Republican candidate; 40 were in favor of the Independent candidate, and 140 were undecided. We want to see if the proportion of voters has changed.
a. Compute the test statistic.
b. Use the p-value approach to test the hypotheses. Let α = .05.
c. Using the critical value approach, test the hypotheses. Let α = .05.

Question 73

In a sample of 40 Democrats, 6 opposed the President's foreign policy, while of 50 Republicans, 8 were opposed to his policy. Determine a 90% confidence interval estimate for the difference between the proportions of the opinions of the individuals in the two parties.

Question 74

Before the rush began for Christmas shopping, a department store had noted that the percentage of its customers who use the store's credit card, the percentage of those who use a major credit card, and the percentage of those who pay cash are the same. During the Christmas rush in a sample of 150 shoppers, 46 used the store's credit card; 43 used a major credit card; and 61 paid cash. With α = 0.05, test to see if the methods of payment have changed during the Christmas rush.

Question 75

In the last presidential election, before the candidates started their major campaigns, the percentages of registered voters who favored the various candidates were as follows.
After the major campaigns began, a random sample of 400 voters showed that 172 favored the Republican candidate; 164 were in favor of the Democratic candidate; and 64 favored the Independent candidate. We are interested in determining whether the proportion of voters who favored the various candidates had changed.
a. Compute the test statistic.
b. Using the p-value approach, test to see if the proportions have changed.
c. Using the critical value approach, test the hypotheses.

Question 76

The results of a recent study regarding smoking and three types of illness are shown in the following table.
$$\begin{array} { l r r r } \text { Illness } & \text { Nom-Smokers } & \text { Smokers } & \text { Totals } \\\text { Emphysema } & 20 & 60 & 80 \\\text { Heart problem } & 70 & 80 & 150 \\\text { Cancer } & 30 & 40 & 70 \\\text { Totals } & 120 & 180 & 300\end{array}$$ We are interested in determining whether or not illness is independent of smoking.
a. State the null and alternative hypotheses to be tested.
b. Show the contingency table of the expected frequencies.
c. Compute the test statistic.
d. The null hypothesis is to be tested at 95% confidence. Determine the critical value for this test. What do you conclude?
e. Determine the p-value and perform the test.

Question 77

The reliability of two types of machines used in the same manufacturing process is to be tested. The first machine failed to operate correctly in 90 out of 300 trials while the second type failed to operate correctly in 50 out of 250 trials.
a. Give a point estimate for the difference between the population proportions of these machines.
b. Calculate the pooled estimate of the population proportion.
c. Carry out a hypothesis test to check whether there is a statistically significant difference in the reliability for the two types of machines using a .10 level of significance.

Question 78

Last school year, in the school of Business Administration, 30% were Accounting majors, 24% Management majors, 26% Marketing majors, and 20% Economics majors. A sample of 300 students taken from this year's students of the school showed the following number of students in each major:
We want to see if there has been a significant change in the number of students in each major.
a. Compute the test statistic.
b. Has there been any significant change in the number of students in each major between the last school year and this school year. Use the p-value approach and let α = .05.

Question 79

In a random sample of 200 Republicans, 160 opposed the new tax laws. While in a sample of 120 Democrats, 84 opposed the new tax laws. Determine a 95% confidence interval estimate for the difference between the proportions of Republicans and Democrats opposed to this new law.

Question 80

From production line A, a sample of 500 items is selected at random, and it is determined that 30 items are defective. In a sample of 300 items from production process B which produces identical items to line A), there are 12 defective items. Determine a 95% confidence interval estimate for the difference between the proportion of defectives in the two lines.