Question 1

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:
$\begin{array} { l l } 
\text { Group Comparison } & 98.33 \% \text { Confidence Interval } \
\text { Type A - Type B } & ( - 12.70 , - 4.29 ) \
\text { Type A - Type C } & ( - 19.63 , - 8.87 ) \
\text { Type B - Type C } & ( - 9.89 , - 1.61 )
\end{array}$
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)  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. 
B)  Yes, the confidence interval results show that frame type A is the faster than B or C. 
C)  Yes, the confidence interval results show that frame type B is the faster than A or C. 
D)  Yes, the confidence interval results show that frame type C is the faster than A or B.

Question 2

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. One-way ANOVA
Variation between groups $= 2063.33$
Variation within groups $= 196.25$
$\mathrm { p } = 4.5985705 \mathrm { E } - 4$
-Choose the correct conclusion for the hypothesis that vehicle color affects the amount of a speeding ticket. Assume all ANOVA test conditions have been satisfied.

Accepted Answer

A)  Reject $\mathrm { H } _ { 0 }$. The vehicle color has no effect on the amount of the speeding ticket. 
B)  Fail to reject $\mathrm { H } _ { 0 }$. The vehicle color has an effect on the amount of the speeding ticket. 
C)  Fail to reject $\mathrm { H } _ { 0 }$. The vehicle color has no effect on the amount of the speeding ticket. 
D)  Reject $\mathrm { H } _ { 0 }$. The vehicle color has an effect on the amount of the speeding ticket.

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. One-way ANOVA
$\mathrm { F } = 0.762135$
$P = 0.5202354$
Factor
$\mathrm { df } = 2$
$\mathrm { SS } = 710.349206$
$\mathrm { MS } = 355.174603$
-State the null and alternative hypothesis.

Accepted Answer

A)  $\mathrm { H } _ { 0 }$ : The mean number of tomatoes harvested differs by type of fertilizer used.
$\mathrm { H } _ { \mathrm { a } }$ : There is no difference in the mean number of tomatoes harvested by type of fertilizer used. 
B)  $\mathrm { H } _ { 0 } : \mu _ { \text {none } } < \mu _ { \text {commercial } } < \mu _ { \text {compost } }$
$\mathrm { H } _ { \mathrm { a } }$ : There is no difference in the mean number of tomatoes harvested. 
C)  $\mathrm { H } _ { 0 } : \mu _ { \text {none } } = \mu _ { \text {commercial } } = \mu _ { \text {compost } }$
$\mathrm { H } _ { \mathrm { a } }$ : The mean number of tomatoes harvested differs by type of fertilizer used.. 
D)  None of these

Question 4

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 5

Which of the following is not one of the conditions that must be checked in order for the calculated F-statistic to follow the F-distribution.

Accepted Answer

A)  The groups are independent of each other. 
B)  The distribution of the observations is Normal in each group's population or the sample size is large. 
C)  The variances or standard deviations of the groups must be equal. 
D)  Each group's population must be at least 10 times larger than its respective sample.

Question 6

Choose the appropriate test for the following situation:
 Suppose that researchers wish to study whether dieting affects alertness levels. Three popular dieting plans were included in the study. After following the diet for several weeks, participants were given a test that measured response time to a stimulus.

Accepted Answer

The answer of Choose the appropriate test for the following...

Question 7

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

Accepted Answer

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

Question 8

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. One-way ANOVA
Variation between groups $= 2063.33$
Variation within groups=196.25
$\mathrm { p } = 4.5985705 \mathrm { E } - 4$
-Compute the F-statistic. Round to the nearest hundredth.

Accepted Answer

A)  0.10 
B)  Not enough information is given 
C)  35.48 
D)  10.51

Question 9

Choose the statement that best describes the F-statistic for the ANOVA test.

Accepted Answer

A)  The F-statistic is the probability of getting the sample results, assuming that there is no difference in the groups. 
B)  The F-statistic compares the variation between groups to the variation within groups. A small F-statistic indicates that variation between groups is large relative to variation within groups. 
C)  The F-statistic compares the variation between groups to the variation within groups. A small F-statistic indicates that variation between groups is small relative to variation within
Groups. 
D)  None of these

Question 10

Suppose a researcher collected data to compare whether cats of different size categories differed in mean number of hours slept per day. Cats were categorized as small, medium, or large. The calculated F-statistic was 220.41. Given this test statistic, can we conclude that there is more variation between groups or within groups?
 Based on the test statistic, is it likely that an association exists between cat size and mean number of hours that a cat sleeps per day?
 Explain.

Accepted Answer

The answer of Suppose a researcher collected data to compare...

Question 11

Use the following information for the question. Researchers conducted a study that examined marital status and work hours. A hypothesis test was conducted to test the claim that people with different marital statuses have a different mean number of work hours. Participants were categorized as married, single, or divorced. Assume that all conditions for the ANOVA test have been met. The TI-84 output for the test is shown below. $$\begin{array} { | }  \text { One-way ANOVA } \ \mathrm { F } = 7.010859729 \ p = 007083712 \ \text { Factor } \ \mathrm { df } = 2 \ \mathrm { SS } = 860.777778 \ \mathrm { MS } = 430.388889 \end{array}$$
-What is the value of the test statistic?
 Round to the nearest hundredth if necessary.

Accepted Answer

The answer of Use the following information for the question....

Question 12

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 13

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:
 $$\begin{array} { l c }  \text { Group Comparison } & 98.33 \% \text { Confidence Interval } \ \text { Type A - Type B } & ( - 12.70 , - 4.29 ) \ \text { Type A - Type C } & ( - 19.63 , - 8.87 ) \ \text { Type B - Type C } & ( - 9.89 , - 1.61 ) \end{array}$$ Is there evidence that one type of bike frame is faster than the others?
 Which type of frame appears To be the fastest?
 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.

Accepted Answer

The answer of An ANOVA test was conducted to see...

Question 14

In the context of the ANOVA test, which of the following phrases is equivalent to the phrase "variation within groups?"

Accepted Answer

A)  Residual variation 
B)  Unexplained variation 
C)  Variation due to error 
D)  All of these

Question 15

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. Using the Bonferroni Correction,
What significance level should you use for each hypothesis test if you want an overall significance
Of 0.05? Round to the nearest thousandth.

Accepted Answer

A)  0.005 
B)  0.050 
C)  0.010 
D)  None of these

Question 16

Choose the appropriate test for the following situation:
 You wish to test whether an association exists between type of vehicle transmission purchased--automatic or manual--and gender of the purchaser.

Accepted Answer

The answer of Choose the appropriate test for the following...

Question 17

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. One-way ANOVA
$
\begin{array}{l}
\mathrm{F}=12.57818941 \
P=2.5637132 E-4
\end{array}
$
Factor
$
\begin{array}{l}
\mathrm{df}=2 \
\mathrm{SS}=710.349206 \
\mathrm{MS}=355.174603
\end{array}
$

-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 $\mathrm { H } _ { 0 }$. We can conclude that the treatment of the soil affects the number of heirloom tomatoes harvested. 
B)  Fail to reject $\mathrm { H } _ { 0 }$. We can conclude that the treatment of the soil does not affect the number of heirloom tomatoes harvested. 
C)  Reject $\mathrm { H } _ { 0 }$. We can conclude that the treatment of the soil does not affect the number of heirloom tomatoes harvested. 
D)  Fail to reject $\mathrm { H } _ { 0 }$. We can conclude that the treatment of the soil affects the number of heirloom tomatoes harvested.

Question 18

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. 
$\begin{array} { | } 
\hline \text { One-way ANOVA } \
\mathrm { F } = 0.762135 \
P = 0.5202354 \
\text { Factor } \
\mathrm { df } = 2 \
\mathrm { SS } = 710.349206 \
\mathrm { MS } = 355.174603 \
\hline
\end{array}$
-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)  Fail to reject $\mathrm { H } _ { 0 }$. We can conclude that the treatment of the soil does not affect the number of heirloom tomatoes harvested. 
B)  Reject $\mathrm { H } _ { 0 }$. We can conclude that the treatment of the soil does not affect the number of heirloom tomatoes harvested. 
C)  Fail to reject $\mathrm { H } _ { 0 }$. We can conclude that the treatment of the soil affects the number of heirloom tomatoes harvested. 
D)  Reject $\mathrm { H } _ { 0 }$. We can conclude that the treatment of the soil affects the number of heirloom tomatoes harvested.

Question 19

Use the following information for the question. Researchers conducted a study that examined marital status and stress levels.
A hypothesis test was conducted to test the claim that people with different marital statuses have a different mean stress
level. The TI-84 output for the test is shown below. $$\begin{array} { c } 
\text { One-way ANOVA } \
\mathrm { F } = 5.21104034 \
P = .0105994136 \
\text { Factor } \
\mathrm { df } = 3 \
\mathrm { SS } = 76.7 \
\mathrm { MS } = 25.5666667
\end{array}$$
-What is the value of the test statistic? Round to the nearest hundredth if necessary.

Accepted Answer

A)  5.21 
B)  76.70 
C)  Can't be determined with the given information 
D)  25.27

Question 20

Choose the appropriate test for the following situation: You wish to test whether an association exists between type of vehicle purchased and vehicle color.

Accepted Answer

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

Exam 11: Multiple Comparisons and Analysis of Variance

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?