Exam 11: Multiple Comparisons and Analysis of Variance

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: Group Comparison 98.33\% Confidence Interval Type A - Type B (-12.70,-4.29) Type A - Type C (-19.63,-8.87) Type B - Type C (-9.89,-1.61) Is there evidence that one type of bike frame is faster than the others? Which type of frame appears To be the fastest?

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.

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.

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?

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 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.

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

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.

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

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.

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. One-way ANOVA =7.010859729 p=007083712 Factor =2 =860.777778 =430.388889 -What is the value of the test statistic? Round to the nearest hundredth if necessary.

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?

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: Group Comparison 98.33\% Confidence Interval Type A - Type B (-12.70,-4.29) Type A - Type C (-19.63,-8.87) Type B - Type C (-9.89,-1.61) 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.

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

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.

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.

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 =12.57818941 P=2.5637132E-4 Factor =2 =710.349206 =355.174603 -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.

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 =0.762135 P=0.5202354 Factor =2 =710.349206 =355.174603 -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.

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. One-way ANOVA =5.21104034 P=.0105994136 Factor =3 =76.7 =25.5666667 -What is the value of the test statistic? Round to the nearest hundredth if necessary.

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