Question 1

Find the value of the $\chi ^ { 2 }$ test statistic for a hypothesis test of independence. Round your answer to 3 decimal places.
-Responses to a survey question are broken down according to gender and the sample results are given below. 
$$\begin{array} { l | c c c } 
& \text { Yes } & \text { No } & \text { Undecided } \
\hline \text { Male } & 25 & 50 & 15 \
\text { Female } & 20 & 30 & 10
\end{array}$$

Accepted Answer

A)  0.749
B)  0.579
C)  0.759
D)  0.921  B

Question 2

You want to estimate the average gasoline price in your city for a gallon of regular gasoline. You take a simple random sample of prices from 17 gasoline stations, recording an average cost of $2.07 and a standard deviation of $0.06. Assume that the population of these prices is normally distributed. Construct the 95% confidence interval estimate of the population mean. Round your estimates to the nearest cent.

Accepted Answer

A)    $2.01<μ<$2.13\$ 2.01 < \mu < \$ 2.13$2.01<μ<$2.13 
B)    $2.06<μ<$2.08\$ 2.06 < \mu < \$ 2.08$2.06<μ<$2.08 
C)    $2.04<μ<$2.10\$ 2.04 < \mu < \$ 2.10$2.04<μ<$2.10 
D)    $2.04<μ<$2.08\$ 2.04 < \mu < \$ 2.08$2.04<μ<$2.08 C

Question 3

Calculate the indicated expected frequency to the nearest whole number.
-The two-way table summarizes data from a survey at a small liberal arts college:

Assuming that status and gender are independent, what is the expected frequency of tenure track men?

Accepted Answer

A)   20
B)   18
C)   16
D)   7 B

Question 4

Solve the problem.
-An industrial psychologist is investigating the effects of work environment on employee attitudes. A group of 20 recently hired sales trainees were randomly assigned to one of four different "home rooms" - five trainees
Per room. Each room is identical except for wall color. The four colors used were light green, light blue, gray and red. The psychologist wants to know whether room color has an effect on attitude, and, if so, wants to compare the mean attitudes of the trainees assigned to the four room colors. At the end of the training program, The attitude of each trainee was measured on a 60-pt. scale (the lower the score, the poorer the attitude). The data was subjected to a one-way analysis of variance. $$\begin{array}{l}
\text { ONE-WAY ANOVA FOR ATTITUDE BY COLOR }\
\begin{array} { l | c | r | r | r | r } 
 { \text { SOURCE } } & \text { DF } &  { \text { SS } } & { \text { MS } } &  { \text { F } } & \text { P-value } \
\hline \text { Between Groups } & 3 & 1678.15 & 559.3833 & 59.03782 & 0.8124 \
\text { Within Groups } & 16 & 151.6 & 9.475 & & \
\text { Total } & 19 & 1829.75 & & &
\end{array}
\end{array}$$
Based on this test, is there sufficient evidence to support the claim that the population means are not equal? Assume that
A 0.05 significance level is used.

Accepted Answer

A)  Yes
B)  No

Question 5

Using a significance level of 0.05, test the claim that the two variables are independent. State whether the variables are related or not related.
-160 students who were majoring in either math or English were asked a test question, and the researcher recorded whether they answered the question correctly. The sample results are given below. $$\begin{array} { l | c c } 
& \text { Correct } & \text { Incorrect } \
\hline \text { Math } & 27 & 53 \
\text { English } & 43 & 37
\end{array}$$

Accepted Answer

A)  related
B)  not related

Question 6

Using a significance level of 0.05, test the claim that the two variables are independent. State whether the variables are related or not related.
-Tests for adverse reactions to a new drug yielded the results given in the table.
 $$\begin{array} { l | c c } 
& \text { Drug } & \text { Placebo } \
\hline \text { Headaches } & 11 & 7 \
\text { No headaches } & 73 & 91
\end{array}$$

Accepted Answer

A)  related
B)  not related

Question 7

Determine the null and alternative hypotheses for the study that produced the data in the table.
-A researcher performed a study to determine whether an association exists between retirement age and career. she obtained the following sample data.

Accepted Answer

A)    H0\mathrm { H } _ { 0 }H0​  : Age at retirement and career are independent. Ha\mathrm { H } _ { \mathrm { a } }Ha​  : There is no relationship between age at retirement and career.
B)    H0\mathrm { H } _ { 0 }H0​  : There is some relationship between age at retirement and career. Ha\mathrm { H } _ { \mathrm { a } }Ha​  : Age at retirement and career are independent.
C)    H0\mathrm { H } _ { 0 }H0​  : Age at retirement and career are independent. Ha\mathrm { H } _ { \mathrm { a } }Ha​  : There is some relationship between age at retirement and career.
D)    H0\mathrm { H } _ { 0 }H0​  : There is some relationship between age at retirement and career. Ha\mathrm { H } _ { \mathrm { a } }Ha​  : Age at retirement and career are not independent.

Question 8

Solve the problem.
-$$\begin{array} { l c c c c c } 
\text { Source } & \text { DF } & \text { SS } & \text { MS } & \text { F } & \text { P-value } \
\text { Factor } & 3 & 13.500 & 4.500 & 5.17 & 0.011 \
\text { Error } & 16 & 13.925 & 0.870 & & \
\text { Total } & 19 & 27.425 & & &
\end{array}$$ Identify the P-value in this display.

Accepted Answer

A)  0.870
B)  4.500
C)  5.17
D)  0.011

Question 9

Find the value of the $\chi ^ { 2 }$ test statistic for a hypothesis test of independence. Round your answer to 3 decimal places.
-A medical researcher is interested in determining if there is a relationship between adults over 50 who walk regularly and low, moderate, and high blood pressure. A random sample of 236 adults over 50 is selected and the results are given below. $$\begin{array} { l | c c c } 
\text { Blood Pressure } & \text { Low } & \text { Moderate } & \text { High } \
\hline \text { Walkers } & 35 & 62 & 25 \
\text { Non-walkers } & 21 & 65 & 28
\end{array}$$

Accepted Answer

A)  9.210
B)  0.176
C)  3.473
D)  3.743

Question 10

Test whether he given claim is supported or not supported using a 0.05 significance level. Assume that the sample has been randomly selected from a population with a normal distribution.
-A trucking firm suspects that the mean life of a certain tire it uses is less than 34,000 miles. To check the claim, the firm randomly selects and tests 18 of these tires and gets a mean lifetime of 33,400 miles with a standard deviation of 1200 miles. Use a 0.05 significance level to test whether the trucking firm's claim is supported or not supported.

Accepted Answer

A)  supported
B)  not supported

Question 11

How tall is your average statistics classmate? To determine this, you measure the height of a simple random sample of 38 fellow students, finding a mean height of 68 inches and a standard deviation of 2.3 inches. Construct the 95% confidence interval estimate of the population mean.

Accepted Answer

A)    68.268.268.2  in.  <μ<68.8< \mu < 68.8<μ<68.8  in.
B)    67.267.267.2  in.  <μ<68.8< \mu < 68.8<μ<68.8  in.
C)    67.267.267.2  in.  <μ<69.8in< \mu < 69.8 \mathrm { in }<μ<69.8in .
D)    68.268.268.2  in.  <μ<69.8< \mu < 69.8<μ<69.8  in.

Question 12

Determine the null and alternative hypotheses for the study that produced the data in the table.
-A researcher performed a study to determine whether an association exists between political party affiliation and income. She obtained the following sample data.

Accepted Answer

A)    H0\mathrm { H } _ { 0 }H0​  : Income bracket and party affiliation are independent.  Ha\mathrm { H } _ { \mathrm { a } }Ha​  : Income bracket and party affiliation are somehow related.
B)    H0\mathrm { H } _ { 0 }H0​  : Income bracket and party affiliation are somehow related.  Ha\mathrm { H } _ { \mathrm { a } }Ha​  : Income bracket and party affiliation are not independent.
C)    H0\mathrm { H } _ { 0 }H0​  : Income bracket and party affiliation are independent.  Ha\mathrm { H } _ { \mathrm { a } }Ha​  : Income bracket and party affiliation are not related.
D)    H0\mathrm { H } _ { 0 }H0​  : Income bracket and party affiliation are somehow related. Ha\mathrm { H } _ { \mathrm { a } }Ha​  : Income bracket and party affiliation are independent.

Question 13

Use software to conduct the analysis of variance test. Use a significance level of 0.05 to test the null hypothesis.
-The grade point averages of students participating in sports at a local college are to be compared. The data are listed below. Do the data indicate that there is a difference in mean grade point average for the three groups? 
$$\begin{array} { c | c | c } 
\text { Tennis } & \text { Golf } & \text { Swimming } \
\hline 2.6 & 1.8 & 2.7 \
3.2 & 3.3 & 3.0 \
2.5 & 1.9 & 2.8 \
3.5 & 2.1 & 2.5 \
3.1 & 1.9 & 2.5 \
2.1 & 2.4 & 2.6
\end{array}$$

Accepted Answer

A)  Yes
B)  No

Question 14

Assume that the results of a yes/no survey question given to a random sample of male and female subjects are summarized in a 2 × 2 two-way table. Use the given values of the test statistic and the significance level to test for
independence between gender and response.
-Given a test statistic of $\chi ^ { 2 } = 7.7$ and a significance level = 0.01, decide whether gender and response are related
Or not related.

Accepted Answer

A)  related
B)  not related

Question 15

A laboratory tested a simple random sample of twelve chicken eggs and found that the mean amount of cholesterol was 215 milligrams with s = 19.8 milligrams. Assume that the population of these amounts is normally distributed. Construct the 95% confidence interval estimate of the population mean.

Accepted Answer

A)    199.5mg<μ<230.5mg199.5 \mathrm { mg } < \mu < 230.5 \mathrm { mg }199.5mg<μ<230.5mg 
B)    209.3mg<μ<220.7mg209.3 \mathrm { mg } < \mu < 220.7 \mathrm { mg }209.3mg<μ<220.7mg 
C)    204.7mg<μ<225.3mg204.7 \mathrm { mg } < \mu < 225.3 \mathrm { mg }204.7mg<μ<225.3mg 
D)    202.4mg<μ<227.6mg202.4 \mathrm { mg } < \mu < 227.6 \mathrm { mg }202.4mg<μ<227.6mg

Question 16

Use software to conduct the analysis of variance test. Use a significance level of 0.05 to test the null hypothesis.
-Random samples of four different models of cars were selected and the gas mileage of each car was measured. The results are shown below. $\begin{array}{cccc}
 \underline{\text { Model A}}& \underline{\text {  Model B}}&  \underline{\text { Model C}}&  \underline{\text { Model D }}\ 
21 & 28 & 30 & 25 \
25 & 26 & 28 & 26 \
24 & 29 & 32 & 25 \
26 & 30 & 27 & 28
\end{array}$
Do the data indicate that there is a difference in mean mileage for the different car models?

Accepted Answer

A)  Yes
B)  No

Question 17

Among a simple random sample of 12 students selected from one college, the mean number of siblings is 1.3 with a standard deviation of 1.1. Construct the 95% confidence interval estimate of the population mean.

Accepted Answer

A)    1.1<μ<1.51.1 < \mu < 1.51.1<μ<1.5 
B)    0.66<μ<1.90.66 < \mu < 1.90.66<μ<1.9 
C)    10.1<μ<13.910.1 < \mu < 13.910.1<μ<13.9 
D)    1.0<μ<1.61.0 < \mu < 1.61.0<μ<1.6

Question 18

Find the value of the $\chi ^ { 2 }$ test statistic for a hypothesis test of independence. Round your answer to 3 decimal places.
-160 students who were majoring in either math or English were asked a test question, and the researcher recorded whether they answered the question correctly. The sample results are given below. $$\begin{array} { l | c c } 
& \text { Correct } & \text { Incorrect } \
\hline \text { Math } & 27 & 53 \
\text { English } & 43 & 37
\end{array}$$

Accepted Answer

A)  0.011
B)  6.205
C)  6.635
D)  6.502

Question 19

A sociologist develops a test to measure attitudes about public transportation, and a simple random sample of 27 subjects are given the test. Their mean score is 76.2 and their standard deviation is 21.6. Assume that the population of these scores is normally distributed. Construct the 95% confidence interval estimate of the population mean.

Accepted Answer

A)    64.2<μ<88.264.2 < \mu < 88.264.2<μ<88.2 
B)    69.2<μ<83.269.2 < \mu < 83.269.2<μ<83.2 
C)    67.7<μ<84.767.7 < \mu < 84.767.7<μ<84.7 
D)    74.6<μ<77.874.6 < \mu < 77.874.6<μ<77.8

Question 20

Using a significance level of 0.05, test the claim that the two variables are independent. State whether the variables are related or not related.
-A medical researcher is interested in determining if there is a relationship between adults over 50 who walk regularly and low, moderate, and high blood pressure. A random sample of 236 adults over 50 is selected and the results are given below. $$\begin{array} { l | c c c } 
\text { Blood Pressure } & \text { Low } & \text { Moderate } & \text { High } \
\hline \text { Walkers } & 50 & 62 & 25 \
\text { Non-walkers } & 21 & 65 & 28
\end{array}$$

Accepted Answer

A)  related
B)  not related

Exam 10: T Tests, Two-Way Tables, and Anova

Calculate the indicated expected frequency to the nearest whole number. -The two-way table summarizes data from a survey at a small liberal arts college: Assuming that status and gender are independent, what is the expected frequency of tenure track men?

Determine the null and alternative hypotheses for the study that produced the data in the table. -A researcher performed a study to determine whether an association exists between retirement age and career. she obtained the following sample data.

How tall is your average statistics classmate? To determine this, you measure the height of a simple random sample of 38 fellow students, finding a mean height of 68 inches and a standard deviation of 2.3 inches. Construct the 95% confidence interval estimate of the population mean.

Determine the null and alternative hypotheses for the study that produced the data in the table. -A researcher performed a study to determine whether an association exists between political party affiliation and income. She obtained the following sample data.

A laboratory tested a simple random sample of twelve chicken eggs and found that the mean amount of cholesterol was 215 milligrams with s = 19.8 milligrams. Assume that the population of these amounts is normally distributed. Construct the 95% confidence interval estimate of the population mean.

Among a simple random sample of 12 students selected from one college, the mean number of siblings is 1.3 with a standard deviation of 1.1. Construct the 95% confidence interval estimate of the population mean.