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. 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

The F-statistic can be computed by dividing the variation between groups by the variation within groups: F = 2063.33/196.25 = 10.51 (rounded to the nearest hundredth). Therefore, the answer is D.

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 $= 462.5$
Variation within groups $= 388.54$ $\mathrm { p } = .3547790947$
-Do the ANOVA test results warrant a Post-hoc procedure?

Accepted Answer

The p-value for the ANOVA test is greater than the commonly used threshold of 0.05, indicating that there is not significant evidence to reject the null hypothesis that the means of the ticket amounts are equal across the four color groups. Therefore, there is no need for a post-hoc procedure to determine which groups differ significantly from each other.

Question 3

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

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

Question 4

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

Accepted Answer

The answer of Choose the statement that is not true...

Question 5

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

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

Question 6

Compute the F-statistic. Round to the nearest hundredth.

Accepted Answer

The question is asking for the F-statistic, but no data is given to calculate it. Therefore, the answer must be B because it is the only provided value.

Question 7

Choose the statement that best describes the purpose of ANOVA.

Accepted Answer

The answer of Choose the statement that best describes the...

Question 8

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

Accepted Answer

All of these phrases are equivalent to the phrase "variation between groups" in the context of the ANOVA test. The ANOVA test is used to determine if there is a significant difference between the means of two or more groups, and the variation between groups (or due to treatment or factors) is what is being compared to the variation within each group (or unexplained variation). Therefore, all three phrases are used to describe the same type of variation in the ANOVA test.

Question 9

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 $= 462.5$
Variation within groups $= 388.54$
$\mathrm { p } = .3547790947$
-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

The p-value of 0.3547790947 is greater than 0.05, so we fail to reject the null hypothesis. This means that there is not enough evidence to conclude that vehicle color affects the amount of a speeding ticket.

Question 10

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

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

Question 11

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? $$\begin{array} { | l l l l l | } 
\hline \text { One-way ANOVA } & & & & \
\mathrm { F } = 15.44055794 & \text { Cat } & \mathrm { n } & \text { Mean } & \text { StDev } \
\mathrm { p } = 7.5111227 \mathrm { E } - 5 & 17 - 24 & 20 & 9.5 & 6.02 \
\text { Factor } & 25 - 32 & 12 & 14.7 & 4.82 \
\mathrm { df } = 2 & 33 - 40 & 21 & 6.5 & 10.21 \
\mathrm { SS } = 1957.90476 & & & & \
\mathrm { MS } = 978.952381 & & & & \
\text { Error } & & & & \
\mathrm { df } = 21 & & & & \
\mathrm { SS } = 1331.42857 & & & & \
\mathrm { MS } = 63.4013605 & & & & \
\mathrm { Sxp } = 7.96249713 & & & & \
\hline
\end{array}$$

Accepted Answer

The answer of A movie studio did a poll to...

Question 12

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

The p-value (2.5637132E-4) is less than the significance level (0.05), so we reject the null hypothesis. This means that we can conclude that the treatment of the soil affects the number of heirloom tomatoes harvested.

Question 13

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

The requirement that each group's population must be at least 10 times larger than its respective sample is not necessary for the calculated F-statistic to follow the F-distribution. The other conditions (normality or large sample size, equality of variances, and independence of groups) must be met.

Question 14

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

The value of the test statistic for a one-way ANOVA is the F-value, which in this case is given to be 5.21104034. Therefore, the answer is choice A) 5.21, rounded to the nearest hundredth.

Question 15

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

Accepted Answer

The answer of Choose the statement that best describes the...

Question 16

Choose the statement that best describes the purpose of ANOVA.

Accepted Answer

ANOVA (Analysis of Variance) is a statistical method used to test whether there are significant differences between the means of three or more groups. Therefore, statement A is the correct answer as it accurately describes the purpose of ANOVA.

Question 17

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

Accepted Answer

The test statistic used for the ANOVA procedure is F, and it is calculated by taking the ratio of the variation between groups to the variation within groups. This ratio is computed by dividing the mean square between groups by the mean square within groups.

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. 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

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

Question 19

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

The appropriate test for this situation is a two-sample t-test because we are comparing the means of two independent groups (males and females) and looking for a significant difference.

Question 20

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 high F-statistic indicates that the variation between group means is larger than the variation within groups, suggesting an association between dog size and mean cost to the pet owner.

Quiz 11: Multiple Comparisons and Analysis of Variance

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

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?

Compute the F-statistic. Round to the nearest hundredth.

Choose the statement that best describes the purpose of ANOVA.

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

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.

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.

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

Choose the statement that best describes the purpose of ANOVA.

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

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.