STAT 250Project V ANOVA

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Harrisburg Area Community College *

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Statistics

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Apr 3, 2024

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STAT 250 Project V (Optional) Name: Chapter 8: ANOVA to Compare Means I. (10 pts) Two sets of sample data, A and B, are given. Without doing any calculations, indicate which set of sample data, A or B, there is likely to be stronger evidence of difference in the two population means. Give a brief reason, comparing means and variability, for your answer. 1. Dataset A Dataset B Group 1 Group 2 Group 1 Group 2 12 25 15 20 20 18 14 21 8 15 16 19 21 28 15 19 14 14 15 21 X 1 = 15 X 2 = 20 X 1 = 15 X 2 = 20 2. Dataset A Dataset B Group 1 Group 2 Group 1 Group 2 13 18 13 48 14 19 14 49 15 20 15 50 16 21 16 51 17 22 17 52 X 1 = 15 X 2 = 20 X 1 = 15 X 2 = 20 II. (10 pts) Given sample sizes for the groups in a dataset and an outline of an analysis of variance table with some information on the sums of squares. Fill in the missing parts of the table. What is the value of the F-statistic? 3. Three groups with n 1 = 5 ,n 2 = 5 , ∧ n 3 = 5. ANOVA table includes: Source df SS MS F-statistic Groups 120 Error 282 Total 402 4. Four groups with n 1 = 10 ,n 2 = 10 ,n 3 = 10 , ∧ n 4 = 10 . ANOVA table includes: Source df SS MS F-statistic Groups 960

Error 5760 Total 6720 III. (10 pts) Some computer output for an analysis of variance is given. a) How many groups are there? b) State the null and alternative hypothesis. c) What is the p-value? d) Give the conclusion of the test, using a 5% significance level? 5. Source df SS MS F-statistic Groups 3 360.0 120.0 1.60 Error 16 1200.0 75.0 Total 19 1560.0 6. Source df SS MS F-statistic Groups 2 540.0 270.0 8.60 Error 27 847.8 31.4 Total 29 1387.8

IV. (20 pts) A study by Fonken, L., at al., “Light at night increases body mass by shifting time of food intake, ” Proceedings of the National Academy of Sciences, October 26, 2010; 107(43): 18664- 18669, investigates effects of light on mice. The study found that even low-level light at night can interfere with normal eating and sleeping cycles. Furthermore, the study finds that the food is especially fattening if consumed at the wrong time of day, at least in mice. In the study, 27 mice were randomly split into three groups. One group was on a normal light-dark cycle ( LD ), one group had a bright light on all the time ( LL ), and one group had light during the day and dim light at night ( DM ). The dim light was equivalent to having a TV on in a room. The mice in darkness ate most of their food during their active (nighttime) period, matching the behavior of mice in the wild. The mice in both dim light and bright light, however, consumed more than half of their food during the well-lit rest period, when most mice are sleeping. Although the data collected show that the three groups of mice ate approximately the same amount of food and had the same levels of physical activity, the mice exposed to light at night gained substantially more weight, ate a greater percent of calories during the day, and were more likely to be classified as glucose intolerant at the end of the study. 5. One-way ANOVA for Body Mass versus Light for each experimental group summary is as follows: Source df SS MS F-statistic P Light 2 113.08 56.54 8.38 0.002 Error 24 161.84 6.74 Total 26 274.92 a) State the null and alternative hypotheses. b) What is the F-statistic? What is the p-value? What is the conclusion of the test? c) Does there appear to be an association between two variables (body mass and light condition)? If so, discuss the nature of that relationship. Under what light condition do mice appear to gain the most weight? d) Can we conclude that there is a cause-and-effect relationship between the variables? Why or why not?

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STAT 250Project V ANOVA

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