Question 1

Use the following information to answer the question. Researchers want to test whether the color of a vehicle ticketed for speeding has an effect on the amount of the ticket. Four vehicle colors were used for the study-- red, white, black, and silver. Thirty vehicles were randomly assigned to each group. Use the output below to answer the question.
 
-Do the ANOVA test results warrant a Post- hoc procedure?

Accepted Answer

A)  No
B)  Yes A

Question 2

Use the following information for the questions. A group of home gardeners want to test whether the type of soil used to grow carrots has an effect on the number of carrots harvested. Gardeners randomly assigned carrot plants to be grown in soil with no fertilizer, commercial plant food, and homemade compost. All other growing conditions were kept the same. Fifty plants were assigned to each group. At the end of the growing season the number of carrots harvested was counted. Use the output below to answer the question. Assume that all other conditions for the ANOVA test have been met.
 
-Using the test results provided, test the hypothesis that soil treatment affects the number of carrots harvested. Use a significance level of 5%. State the correct decision regarding the null hypothesis and write a sentence summarizing the conclusion.

Accepted Answer

The four conditions are (1)random sample and independent measurements, (2)independent groups, (3)same variance, and (4)Normal distribution or large sample.

Question 3

Use the following information for the question. A group of home gardeners want to test whether the type of soil used to grow heirloom tomatoes has an effect on the number of tomatoes harvested. Gardeners randomly assigned tomato plants to be grown in soil with no fertilizer, commercial plant food, and homemade compost. All other growing conditions were kept the same. Forty plants were assigned to each group. At the end of the growing season the number of tomatoes harvested was counted. Assume that all other conditions for the ANOVA test have been met.
 
-Using the test results provided, test the hypothesis that soil treatment affects the number of tomatoes harvested. Use a significance level of 5%. Choose the correct decision regarding the null hypothesis and correct conclusion.

Accepted Answer

A)  Reject H0. We can conclude that the treatment of the soil affects the number of heirloom tomatoes harvested.
B)  Fail to reject H0. We can conclude that the treatment of the soil does not affect the number of heirloom tomatoes harvested.
C)  Reject H0. We can conclude that the treatment of the soil does not affect the number of heirloom tomatoes harvested.
D)  Fail to reject H0. We can conclude that the treatment of the soil affects the number of heirloom tomatoes harvested. A

Question 4

Choose the appropriate test for the following situation: You wish to test whether an association exists between the type of vehicle purchased and how many children the buyer has.

Accepted Answer

A)  ANOVA
B)  One- sample t- test
C)  Two- sample t- test
D)  Chi- square test

Question 5

Choose the appropriate test for the following situation: You wish to test whether the mean number of words recalled from short term memory is different for males and females.

Accepted Answer

A)  Two- sample t- test
B)  Chi- square test
C)  One- sample t- test
D)  ANOVA

Question 6

A movie studio did a poll to determine whether women in different age groups watched different amounts of horror movies. Check the computer output to see whether the same- variance condition for ANOVA holds. Is ANOVA appropriate?

Accepted Answer

A)  No
B)  Yes

Question 7

Choose the statement that best describes the purpose of ANOVA.

Accepted Answer

A)  ANOVA is a procedure for comparing the means of several groups.
B)  ANOVA is a procedure for comparing different categories for several groups.
C)  The ANOVA procedure will reveal whether the means of several groups are different and which group or groups have a different mean.
D)  None of these

Question 8

State the null and alternative hypothesis.

Accepted Answer

A)  H0: There is no difference in the mean stress levels of married and unmarried people. Ha: There is a difference in the mean stress levels of married and unmarried people.
B)  H0: Marital status and stress levels are associated. Ha: Marital status and stress levels are not associated.
C)  H0: Marital status and stress levels are not associated. Ha: Marital status and stress levels are associated.
D)  H0: Marital status and stress levels are not associated. Ha: Mean stress levels of married people are greater than the mean stress levels of unmarried people.

Question 9

Suppose you have observations from six different school districts within your state and you wish to do hypothesis tests to compare the mean home value across groups. Using the Bonferroni Correction, what significance level should you use for each hypothesis test if you want an overall significance of 0.10? Round to the nearest thousandth.

Accepted Answer

The answer of Suppose you have observations from six different...

Question 10

Suppose a researcher collected data to compare whether dogs of different size categories differed in mean cost to a pet owner. Dogs were categorized as small, medium, or large. Cost was calculated as the average annual amount spent on food, veterinary visits, and medications. The calculated F- statistic was 421.58. Given this test statistic, which of the following is the most reasonable conclusion?

Accepted Answer

A)  The F- statistic shows that variation between groups is larger than variation within groups, therefore, the researcher will likely conclude that there is an association between dog size and mean cost to the pet owner.
B)  The F- statistic shows that large dogs have a significantly higher cost to the pet own than the other categories, therefore, the researcher will conclude that there is an association between dog size and mean cost to the pet owner.
C)  The F- statistic shows that variation within groups is larger than variation between groups, therefore, the researcher will likely conclude that there is not an association between dog size and mean cost to the pet owner.
D)  None of these

Question 11

An ANOVA test was conducted to see whether bike frame type (Type A, Type B, or Type C)had an effect on speed over a one mile distance. Test results warranted post- hoc procedures. The Tukey HSD approach was used with the following results:
 Is there evidence that one type of bike frame is faster than the others? Which type of frame appears to be the fastest?

Accepted Answer

A)  Yes, the confidence interval results show that frame type A is the faster than B or C.
B)  Yes, the confidence interval results show that frame type C is the faster than A or B.
C)  Yes, the confidence interval results show that frame type B is the faster than A or C.
D)  No, there is not enough evidence to say with confidence that one frame type is faster than the others because none of the confidence intervals contain zero.

Question 12

Suppose you have observations from six different regions within your state and you wish to do hypothesis tests to compare the mean income across groups. How many comparisons can be done with six groups?

Accepted Answer

A)  30
B)  11
C)  15
D)  20

Question 13

A movie studio did a poll to determine whether women in different age groups watched different amounts of horror movies. Check the computer output to see whether the same- variance condition for ANOVA holds. Is ANOVA appropriate?

Accepted Answer

A)  Yes
B)  No

Question 14

Suppose a researcher collected data to compare whether dogs of different size categories differed in mean cost to a pet owner. Dogs were categorized as small, medium, or large. Cost was calculated as the average annual amount spent on food, veterinary visits, and medications. The calculated F- statistic was 421.58. Given this test statistic, which of the following is the most reasonable conclusion?

Accepted Answer

A)  The F- statistic shows that variation within groups is larger than variation between groups, therefore, the researcher will likely conclude that there is not an association between dog size and mean cost to the pet owner.
B)  The F- statistic shows that large dogs have a significantly higher cost to the pet own than the other categories, therefore, the researcher will conclude that there is an association between dog size and mean cost to the pet owner.
C)  The F- statistic shows that variation between groups is larger than variation within groups, therefore, the researcher will likely conclude that there is an association between dog size and mean cost to the pet owner.
D)  None of these

Question 15

Suppose you have observations from six different regions within your state and you wish to do hypothesis tests to compare the mean income across groups. Using the Bonferroni Correction, what significance level should you use for each hypothesis test if you want an overall significance of 0.10? Round to the nearest thousandth.

Accepted Answer

A)  0.050
B)  0.033
C)  0.007
D)  None of these

Question 16

Suppose you have observations from five different regions within your state and you wish to do hypothesis tests to compare the mean home value across groups. How many comparisons can be done with six groups?

Accepted Answer

A)  30
B)  20
C)  15
D)  10

Question 17

Choose the statement that best describes the purpose of ANOVA.

Accepted Answer

A)  ANOVA is a procedure for comparing the means of several groups.
B)  The ANOVA procedure will reveal whether the means of several groups are different and which group or groups have a different mean.
C)  ANOVA is a procedure for comparing different categories for several groups.
D)  None of these

Question 18

Choose the statement that is not true about multiple comparisons and ANOVA. Choose (d)if all the statements are true.

Accepted Answer

A)  When doing multiple comparisons, the response variable is always numerical, but the independent variable can be numerical or categorical.
B)  When doing a multiple comparison, the overall significance level will increase meaning it is more likely that an incorrect conclusion will be drawn.
C)  ANOVA is a method for testing whether there is an association between a categorical variable and a numerical variable.
D)  All of these statements are true.

Question 19

In the context of the ANOVA test, do the phrases "variation due to treatment", "explained variation", and "variation due to factors", describe variation within groups or variation between groups?

Accepted Answer

The answer of In the context of the ANOVA test,...

Question 20

Identify the test statistic used for the ANOVA procedure and how it is calculated.

Accepted Answer

A)  The test statistic is z and is the ratio of the mean within a group to the variation between groups.
B)  The test statistic is z and is calculated by finding the mean z- score between groups.
C)  The test statistic is F and is the ratio of the variation between groups to the variation within groups.
D)  The test statistic is F and is calculated by finding the difference between group means.

Exam 11: Multiple Comparisons and Analysis of Variance

Choose the appropriate test for the following situation: You wish to test whether an association exists between the type of vehicle purchased and how many children the buyer has.

Choose the appropriate test for the following situation: You wish to test whether the mean number of words recalled from short term memory is different for males and females.

A movie studio did a poll to determine whether women in different age groups watched different amounts of horror movies. Check the computer output to see whether the same- variance condition for ANOVA holds. Is ANOVA appropriate?

Choose the statement that best describes the purpose of ANOVA.

State the null and alternative hypothesis.

Suppose you have observations from six different regions within your state and you wish to do hypothesis tests to compare the mean income across groups. How many comparisons can be done with six groups?

A movie studio did a poll to determine whether women in different age groups watched different amounts of horror movies. Check the computer output to see whether the same- variance condition for ANOVA holds. Is ANOVA appropriate?

Suppose you have observations from five different regions within your state and you wish to do hypothesis tests to compare the mean home value across groups. How many comparisons can be done with six groups?

Choose the statement that best describes the purpose of ANOVA.

Choose the statement that is not true about multiple comparisons and ANOVA. Choose (d) if all the statements are true.

In the context of the ANOVA test, do the phrases "variation due to treatment", "explained variation", and "variation due to factors", describe variation within groups or variation between groups?

Identify the test statistic used for the ANOVA procedure and how it is calculated.