Deck 12: Tests of Goodness of Fit, Independence and Multiple Proportions

Question 1

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

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

Answer 1

B

Question 2

The sampling distribution for a goodness of fit test is

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

Answer 2

D

Question 3

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.

Answer 3

C

Question 4

Exhibit 12-2
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. 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 12-2. The null hypothesis

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

Question 5

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 6

Exhibit 12-2
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. 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 12-2. The expected frequency of seniors is

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

Question 7

Exhibit 12-1
When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained. 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 12-1. The calculated value for the test statistic equals

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

Question 8

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 9

Exhibit 12-1
When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained. 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 12-1. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals

A)7.37776
B)7.81473
C)5.99147
D)9.34840

Question 10

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 11

Exhibit 12-1
When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained. 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 12-1. The expected frequency for each group is

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

Question 12

Exhibit 12-1
When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained. 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 12-1. The conclusion of the test is that the

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

Question 13

Exhibit 12-2
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. 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 12-2. The calculated value for the test statistic equals

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

Question 14

Exhibit 12-3
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. We are interested in determining whether or not the medication was effective in curing the common cold.
Refer to Exhibit 12-3. The expected frequency of those who received medication and were cured is

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

Question 15

Exhibit 12-1
When individuals in a sample of 150 were asked whether or not they supported capital punishment, the following information was obtained. 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 12-1. The number of degrees of freedom associated with this problem is

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

Question 16

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

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

Question 17

Exhibit 12-2
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. 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 12-2. 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)2.75
D)7.815

Question 18

Exhibit 12-2
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. 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 12-2. The expected number of freshmen is

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

Question 19

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.

Question 20

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 21

Exhibit 12-5
The table below gives beverage preferences for random samples of teens and adults. We are asked to test for independence between age (i.e., adult and teen) and drink preferences.
Refer to Exhibit 12-5. The result of the test is that the

A)hypothesis of independence can be rejected
B)hypothesis of independence cannot be rejected
C)test is inconclusive
D)None of these alternatives is correct.

Question 22

Exhibit 12-6
The following shows the number of individuals in a sample of 300 who indicated they support the new tax proposal. We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed.
Refer to Exhibit 12-6. The expected frequency for each group is

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

Question 23

Exhibit 12-3
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. We are interested in determining whether or not the medication was effective in curing the common cold.
Refer to Exhibit 12-3. The null hypothesis

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

Question 24

Exhibit 12-6
The following shows the number of individuals in a sample of 300 who indicated they support the new tax proposal. We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed.
Refer to Exhibit 12-6. The calculated value for the test statistic equals

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

Question 25

Exhibit 12-3
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. We are interested in determining whether or not the medication was effective in curing the common cold.
The degrees of freedom for a contingency table with 10 rows and 11 columns is

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

Question 26

Exhibit 12-4
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 12-4. The calculated value for the test statistic equals

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

Question 27

Exhibit 12-4
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 12-4. This problem is an example of a

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

Question 28

Exhibit 12-5
The table below gives beverage preferences for random samples of teens and adults. We are asked to test for independence between age (i.e., adult and teen) and drink preferences.
Refer to Exhibit 12-5. The expected number of adults who prefer coffee is

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

Question 29

Exhibit 12-4
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 12-4. The expected frequency for the Business College is

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

Question 30

Exhibit 12-5
The table below gives beverage preferences for random samples of teens and adults. We are asked to test for independence between age (i.e., adult and teen) and drink preferences.
Excel's ____ function is used to perform a goodness of fit test.

A)z-Test: Two Sample for Means
B)t-Test: Two Sample Assuming Equal Variances
C)CHISQ.DIST.RT
D)NORM.S.DIST

Question 31

Exhibit 12-4
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 12-4. The hypothesis is to be tested at the 5% level of significance. The critical value from the table equals

A)1.645
B)19.6
C)5.99
D)7.80

Question 32

Exhibit 12-5
The table below gives beverage preferences for random samples of teens and adults. We are asked to test for independence between age (i.e., adult and teen) and drink preferences.
Excel's ____ function is used to perform a test of independence.

A)z-Test: Two Sample for Means
B)t-Test: Two Sample Assuming Equal Variances
C)CHISQ.TEST
D)NORM.S.DIST

Question 33

Exhibit 12-5
The table below gives beverage preferences for random samples of teens and adults. We are asked to test for independence between age (i.e., adult and teen) and drink preferences.
Refer to Exhibit 12-5. 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 34

Exhibit 12-3
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. We are interested in determining whether or not the medication was effective in curing the common cold.
Refer to Exhibit 12-3. The test statistic is

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

Question 35

Exhibit 12-5
The table below gives beverage preferences for random samples of teens and adults. We are asked to test for independence between age (i.e., adult and teen) and drink preferences.
In a goodness of fit test, Excel's CHISQ.DIST.RT function returns a

A)chi-square critical value
B)chi-square test statistic
C)p-value
D)confidence interval estimate

Question 36

Exhibit 12-3
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. We are interested in determining whether or not the medication was effective in curing the common cold.
Refer to Exhibit 12-3. The number of degrees of freedom associated with this problem is

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

Question 37

Exhibit 12-5
The table below gives beverage preferences for random samples of teens and adults. We are asked to test for independence between age (i.e., adult and teen) and drink preferences.
Refer to Exhibit 12-5. The calculated value for this test for independence is

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

Question 38

Exhibit 12-3
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. We are interested in determining whether or not the medication was effective in curing the common cold.
Refer to Exhibit 12-3. 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 39

Exhibit 12-5
The table below gives beverage preferences for random samples of teens and adults. We are asked to test for independence between age (i.e., adult and teen) and drink preferences.
Excel's CHISQ.DIST function can be used to perform

A)a multinomial goodness of fit test
B)a Poisson distribution goodness of fit test
C)a Normal distribution goodness of fit test
D)All of the other ANSWERs are correct

Question 40

Exhibit 12-4
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 12-4. 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 41

A group of 2000 individuals from 3 different cities were asked whether they owned a foreign or a domestic car. The following contingency table shows the results of the survey.
At $\alpha$ = 0.05, test to determine if the type of car purchased is independent of the city in which the purchasers live.

Question 42

Exhibit 12-6
The following shows the number of individuals in a sample of 300 who indicated they support the new tax proposal. We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed.
The test for goodness of fit, test of independence, and test of multiple proportions are designed for use with

A)categorical data
B)bivariate data
C)quantitative data
D)ordinal data

Question 43

Exhibit 12-6
The following shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.
We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed.

-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:
Has there been any significant change in the number of students in each major between the last school year and this school year? Use $\alpha$ = 0.05.

Question 44

Shown below is a 2 * 3 contingency table with observed values from a sample of 500. At 95% confidence, test for independence of the row and column factors.

Question 45

Exhibit 12-6
The following shows the number of individuals in a sample of 300 who indicated they support the new tax proposal. We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed.
The test for goodness of fit

A)is always a lower-tail test
B)is always an upper-tail test
C)is always a two-tailed test
D)can be a lower- or upper-tail test

Question 46

Shown below is a 3 * 2 contingency table with observed values from a sample of 1,500. At 95% confidence, test for independence of the row and column factors.

Question 47

Exhibit 12-6
The following shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.
We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed.

-A major automobile manufacturer claimed that the frequencies of repairs on all five models of its cars are the same. A sample of 200 repair services showed the following frequencies on the various makes of cars.
At $\alpha$ = 0.05, test the manufacturer's claim.

Question 48

Exhibit 12-6
The following shows the number of individuals in a sample of 300 who indicated they support the new tax proposal. We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed.
Before the presidential debates, it was expected that the percentages of registered voters in favor of various candidates to 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. At a 5% level of significance, test to see if the proportion of voters has changed.

Question 49

Exhibit 12-6
The following shows the number of individuals in a sample of 300 who indicated they support the new tax proposal. We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed.
The properties of a multinomial experiment include all of the following except

A) the experiment consists of a sequence of n identical trials
B) three or more outcomes are possible on each trial
C) the probability of each outcome can change from trial to trial
D) the trials are independent

Question 50

A lottery is conducted that involves the random selection of numbers from 0 to 4. To make sure that the lottery is fair, a sample of 250 was taken. The following results were obtained:
a.State the null and alternative hypotheses to be tested.
b.Compute the test statistic.
c.The null hypothesis is to be tested at the 5% level of significance. Determine the critical value from the table.
d.What do you conclude about the fairness of this lottery?

Question 51

The makers of Compute-All know that in the past, 40% of their sales were from people under 30 years old, 45% of their sales were from people who are between 30 and 50 years old, and 15% of their sales were from people who are over 50 years old. A sample of 300 customers was taken to see if the market shares had changed. In the sample, 100 of the people were under 30 years old, 150 people were between 30 and 50 years old, and 50 people were over 50 years old.
a.State the null and alternative hypotheses to be tested.
b.Compute the test statistic.
c.The null hypothesis is to be tested at the 1% level of significance. Determine the critical value from the table.
d.What do you conclude?

Question 52

Exhibit 12-6
The following shows the number of individuals in a sample of 300 who indicated they support the new tax proposal. We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed.
A medical journal reported the following frequencies of deaths due to cardiac arrest for each day of the week: At a 5% level of significance, determine whether the number of deaths is uniform over the week.

Question 53

Exhibit 12-6
The following shows the number of individuals in a sample of 300 who indicated they support the new tax proposal. We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed.
The number of categories of outcomes per trial for a multinomial probability distribution is

A)two or more
B)three or more
C)four or more
D)five or more

Question 54

A sample of 150 individuals (males and females) was surveyed, and the individuals were asked to indicate their yearly incomes. The results of the survey are shown below. Test at $\alpha$ = 0.05 to determine if the yearly income is independent of the gender.

Question 55

Exhibit 12-6
The following shows the number of individuals in a sample of 300 who indicated they support the new tax proposal. We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed.
In 2012, 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 2013, two hundred were Business majors, 220 were Engineering majors and the remaining students in the sample were majoring in other fields. At a 5% significance level, test to see if there has been a significant change in the proportions between 2012 and 2013.

Question 56

Exhibit 12-6
The following shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.
We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed.

-The personnel department of a large corporation reported sixty resignations during the last year. The following table groups these resignations according to the season in which they occurred:
Test to see if the number of resignations is uniform over the four seasons.Let $\alpha$ = 0.05.

Question 57

Exhibit 12-6
The following shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.
We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed.

-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 $\alpha$ = 0.05, test to see if the methods of payment have changed during the Christmas rush.

Question 58

Exhibit 12-6
The following shows the number of individuals in a sample of 300 who indicated they support the new tax proposal.
We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed.

-In the last presidential election before the candidates began 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. Test with $\alpha$ = .01 to see if the proportion of voters who favored the various candidates changed.

Question 59

Exhibit 12-6
The following shows the number of individuals in a sample of 300 who indicated they support the new tax proposal. We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed.
Refer to Exhibit 12-6. The number of degrees of freedom associated with this problem is

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

Question 60

Exhibit 12-6
The following shows the number of individuals in a sample of 300 who indicated they support the new tax proposal. We are interested in determining whether or not the opinions of the individuals of the three groups are uniformly distributed.
The test statistic for goodness of fit has a chi-square distribution with k - 1 degrees of freedom provided that the expected frequencies for all categories are

A)5 or more
B)10 or more
C)k or more
D)2k

Question 61

One thousand managers with degrees in business administration indicated their fields of concentration as shown below.
Test at $\alpha$ = .01 to determine if the position in management is independent of the major of concentration.

Question 62

The following table shows the results of a study on smoking and three illnesses. We are interested in determining if the proportions smokers in the three categories are different from each other.
a.Provide the null and the alternative hypotheses.
b.Determine the expected frequencies.
c.Compute the sample proportions.
d.Compute the critical values (CV_ij).
e.Give your conclusions by providing numerical reasoning.

Question 63

City planners are evaluating three proposed alternatives for relieving the growing traffic congestion on a north-south highway in a booming city. The proposed alternatives are: (1) designate high-occupancy vehicle (HOV) lanes on the existing highway, (2) construct a new, parallel highway, and (3) construct a light (passenger) rail system.In an analysis of the three proposals, a citizen group has raised the question of whether preferences for the three alternatives differ among residents near the highway and non-residents. A test of independence will address this question, with the hypotheses being:
H₀: Proposal preference is independent of the residency status of the individual
H_a: Proposal preference is not independent of the residency status of the individual
A simple random sample of 500 individuals has been selected. A crosstabulation of the residency statuses and proposal preferences of the individuals sampled is shown below.
Conduct a test of independence using $\alpha$ = .05 to address the question of whether residency status is independent of the proposal preference.

Question 64

A group of 500 individuals were asked to cast their votes regarding a particular issue of the Equal Rights Amendment. The following contingency table shows the results of the votes:
Test at $\alpha$ = .05 to determine if the votes cast were independent of the gender of the individuals.

Question 65

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 $\alpha$ = .05.
c.At 95% confidence, test for a significant difference using the critical value approach.

Question 66

Members of a focus group stated their preferences between three possible slogans. The results follow. Use Excel to test at $\alpha$ = .05 to determine any difference in preference among the three slogans.

Question 67

During "sweeps week" last year, the viewing audience was distributed as follows: 36% NBC, 22% ABC, and 24% CBS, and 18% FOX. This year during "sweeps week" a sample of 50 homes yielded the following data. Use Excel to test at $\alpha$ = .05 to determine if the audience proportions have changed.

Question 68

A study of wage discrimination at a local store compared employees' race and their status. Partial results of the study follow. Use Excel and test at $\alpha$ = .05 to determine if race is independent of status.

Question 69

The data below represents the fields of specialization for a randomly selected sample of undergraduate students. Test to determine whether there is a significant difference in the fields of specialization between regions of the country. Use a .05 level of significance.
a.State the critical value of the chi-square random variable for this test of independence of categories.
b.Calculate the value of the test statistic.
c.What is the conclusion for this test?

Question 70

Dr. Ross' diet pills are supposed to cause significant weight loss. The following table shows the results of a recent study where some individuals took the diet pills and some did not. With 95% confidence, test to see if losing weight is dependent on taking the diet pills.

Question 71

Prior to the start of the season, it was expected that audience proportions for the four major news networks would be CBS 18.6%, NBC 12.5%, ABC 28.9% and BBC 40%. A recent sample of homes yielded the following viewing audience data. We want to determine whether or not the recent sample supports the expectations of the number of homes of the viewing audience of the four networks.
a.State the null and alternative hypotheses to be tested.
b.Compute the test statistic.
c.The null hypothesis is to be tested at 95% confidence. Determine the critical value for this test.
d.What do you conclude?

Question 72

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:
Test at $\alpha$ = .05 to determine if the selection of a TV station is dependent upon the level of education.

Question 73

Shoppers were asked where they do their regular grocery shopping. The table below shows the responses of the sampled shoppers. We are interested in determining if the proportions of females in the three categories are different from each other.
a.Provide the null and the alternative hypotheses.
b.Determine the expected frequencies.
c.Compute the sample proportions.
d.Compute the critical values (CV_ij).
e.Give your conclusions by providing numerical reasoning.

Question 74

Five hundred randomly selected automobile owners were questioned on the main reason they had purchased their current automobile. The results are given below.
a.State the null and alternative hypotheses for a contingency table test.
b.State the decision rule, using a .10 level of significance.
c.Calculate the chi-square test statistic.
d.Give your conclusion for this test.

Question 75

Prior to the start of the season, it was expected that audience proportions for the four major news networks would be CBS 28%, NBC 35%, ABC 22% and BBC 15%. A recent sample of homes yielded the following viewing audience data. We want to determine whether or not the recent sample supports the expectations of the number of homes of the viewing audience of the four networks.
a.State the null and alternative hypotheses to be tested.
b.Compute the test statistic.
c.The null hypothesis is to be tested at 95% confidence. Determine the critical value for this test.
d.What do you conclude?

Question 76

Employee panel preferences for three proposed company logo designs follow.
Use $\alpha$ = .05 and test to determine any difference in preference among the three logo designs.