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Baby weight and smoking Smoking during pregnancy is a known cause of reduced infant birth weight and other issues that can affect the delivery and mortality. Despite this strong evidence, women who smoke find it difficult to quit even when they are pregnant. Suppose a study is done measuring the birth weight of babies of mothers who smoked during pregnancy and those who did not smoke. The birth weight data in pounds are: Smokers: 3.1. 4.2. 4.5, 5.0, 6.4, 4.7, 8.0 Nonsmokers: 5.5, 6.5, 7.1, 8.0. 8.8, 7.5, 6.2 a. State the hypotheses for conducting a one-sided (right tailed) Wilcoxon test. b. Find the ranks for the two groups and their mean ranks. c. Software reports a small-sample one-sided P-value of 0.022. Interpret.Tanning experiment Suppose the tanning experiment described in Examples 1 and 2 used only four participants, two for each treatment. a. Show the six possible ways the four ranks could be allocated, two to each treatment, with no ties. b. For each possible sample, find the mean rank for each treatment and the difference between the mean ranks. c. Presuming HO is true of identical treatment effects, construct the sampling distribution of the difference between the sample mean ranks for the two treatments.\fTelephone holding times In Exercise 1, the telephone holding times for Muzak and classical music were Muzak 0, 1. 4, 6, 3 Classical 13, 9. 8, 15. 7 a. For comparing these two groups with the Wilcoxon test, report the ranks and the mean rank for each group. b. Two groups of size 5 each have 252 possible allocations of rankings. For a two-sided test of HO: identical distributions with these data, explain why the P-value is 2/252 = 0.008. Interpret the P-value. Exercise 1 How long do you tolerate being put on hold? Examples 1-4 and 7 in Chapter 14 referred to the following randomized experiment: An airline analyzed whether telephone callers to their reservations office would remain on hold longer, on average, if they heard (3) an advertisement about the airline, (b) Muzak, or (c) classical music. For 15 callers randomly assigned to these three conditions, the table shows the data. It also shows the ranks for the 15 observations, as well as the mean rank for each group and some results from using MINITAB to conduct the Kruskal-Wallis test a. State the null and alternative hypotheses for the Kruskal Wallis test. b. Identify the value of the test statistic for the Kruskal-Wallis test, and state its approximate sampling distribution, presuming HO is true. c. Report and interpret the P-value shown for the Kruskal-Wallis test. d. To find out which pairs of groups significantly differ, how could you follow up the Kruskal-Wallis lest? Telephone holding times by type of recorded message Recorded Message | Holding Time Observations | Ranks Mean Rank Muzak 0, 1. 3, 4, 6 1, 2, 5, 5, 6, 8 4.5 Advertisement 1, 2, 5, 8, 11 2.5, 4, 7, 10.5, 13 7.4 Classical 7, 8. 9, 13, 15 9, 10.5. 12, 14, 15 12.1 Kruskal-Wallis Test: Holding Time Versus Group Group N Median |Ave Rank Muzak 5 3.000 4.5 Advert 5 5. 000 7.4 Classical | 5 9.000 12.1 H = 7.38 DF = 2 P = 0.025 (adjusted for ties)Teenage anorexia Example 8 in Section 9.3 and Exercise 1 described a study that used therapy to treat teenage girls who suffered from anorexia. The girls were randomly assigned to the cognitive behavioral treatment (Group 1) or to the control group (Group 2). The study observed the weight change after a period of time. The output shows results of a nonparametric comparison. a. Interpret the reported point estimate of the difference between the population medians for the weight changes for the two groups. b. Interpret the reported confidence interval, and summarize the assumptions on which it based c. Report a P-value for testing the null hypothesis of identical population distributions of weight change. Specify the alternative hypothesis, and interpret the P-value. MINITAB output comparing weight changes N Median Cognitive_change | 20 1.400 Control_change 26 -0.350 Point estimate for ETA1-ETA2 is 3.0595.0 Percent CI for ETA1-ETA2 is (-0.80, 8.10)W = 807.0Te Exercise 1 Teenage anorexia Example 8 in Section 9.3 described a study that used a cognitive behavioral therapy to treat a sample of teenage girls who suffered from anorexia. The study observed the mean weight change after a period of treatment. Studies of that type also usually have a control group that receives no treatment or a standard treatment. Then researchers can analyze how the change in weight compares for the treatment group to the control group. In fact, the anorexia study had a control group that received a standard treatment. Teenage girls in the study were randomly assigned to the cognitive behavioral treatment (Group 1) or lo the control group (Group 2). The figure shows box plots of the weight changes for the two groups (displayed vertically). The output shows how MINITAB reports inferential comparisons of those two means. MINITAB Output Comparing Mean Weight Changes group N Mean StDev | SE Mean cog_behav 29 3.01 7.31 1.4 control 6-0.45 7.99 1.8 Difference = mu (cog_behav) - mu (control) Estimate for difference: 3.4569095%% CI for difference 25 15 : 10 cog behay control group Box plots of weight change for anorexia study. a. Report and interpret the P-value for testing HO: p1 = p2 against Ha: p1, # p2. b. Summarize the assumptions needed for the analysis in part a. Based on the box plots, would you be nervous if you had to perform a one-sided test instead? Why? c. The reported 95% confidence interval tells us that if the population mean weight change is less for the cognitive behavioral group than for the control group, it is just barely less (less than 1 pound), but if the population mean change is greater, it could be nearly 8 pounds greater. Explain how to get this interpretation from the interval reported.How long do you tolerate being put on hold? Examples 1-4 and 7 in Chapter 14 referred to the following randomized experiment: An airline analyzed whether telephone callers to their reservations office would remain on hold longer, on average, if they heard (3) an advertisement about the airline, (b) Muzak, or (c) classical music. For 15 callers randomly assigned to these three conditions, the table shows the data. It also shows the ranks for the 15 observations, as well as the mean rank for each group and some results from using MINITAB to conduct the Kruskal-Wallis test a. State the null and alternative hypotheses for the Kruskal Wallis test. b. Identify the value of the test statistic for the Kruskal-Wallis test, and state its approximate sampling distribution, presuming HO is true. c. Report and interpret the P-value shown for the Kruskal-Wallis test. d. To find out which pairs of groups significantly differ, how could you follow up the Kruskal-Wallis lest? Telephone holding times by type of recorded message Recorded Message | Holding Time Observations | Ranks Mean Rank Muzak 0. 1. 3, 4, 8 1. 2. 5, 5, 8. 8 15 Advertisement 1, 2, 5, 8, 11 2.5, 4, 7, 10.5, 13 7.4 Classical 7. 8. 9, 13, 15 9. 10.5, 12, 14. 15 12.1 Kruskal-Wallis Test: Holding Time Versus Group Group N Median|Ave Rank Muzak 5 3.000 1.5 Advert 5 5. 000 7.4 Classical | 5 9.000 12.1 H = 7.38 DF = 2 P = 0.025 (adjusted for ties)What's the best way to learn French? Exercise 1 gave the data in the table for scores on the first quiz for ninthgrade students in an introductory-level French course. The instructor grouped the students in the course as follows: Group 1 : Never studied foreign language before, but have good English skills Group 2: Never studied foreign language before; have poor English skills Group 3: Studied at least one other foreign language The table also shows results of using MINITAB to perform the Kruskal-Wallis test. a. Find the rank associated with each observation, and show how to find the mean rank for Group 1. b. Report and interpret the P-value for the test. Scores on the quiz Group 1 Group 2| Group 3 g 51 10 8 5 Kruskal-Wallis Test on response Group N Median | Ave Rank 8. 000 4.3 2 2 3.000 2.3 3 9.000 8.2 9.000 8.2 H = 3.13 DF = 2 P = 0.209 (adjusted for ties) Exercise 1 What's the best way to learn French? The following table shows scores on the first quiz (maximum score 10 points) for eighth-grade students in an introductory level French course. The instructor grouped the students in the course as follows: Group 1: Never studied foreign language before but have good English skills Group 2: Never studied foreign language before and have poor English skills Group 3: Studied at least one other foreign language French scores on the quiz Group 1 Group 2 Group 3 9 5 5 Mear 60 3.0 8.0 Std. Dev. |2.000 2.828 2.646 Source DE SS MS C Group 3 0.00 15.00 2.50 0.177 Error 5 0.00 |6.00 Total 10.00 Defining notation and using results obtained with software, also shown in the table, report the Ive steps of the ANOVA test. . The sample means are quite different, but the P-value is not small. Name one important eason for this. (Hint: For given sample means, how do the results of the test depend on the sample sizes?) Was this an experimental study. or an observational study? Explain how a lurking variable ould be responsible for Group 3 having a larger mean than the others. (Thus, even if the P- value were small, it is inappropriate to assume that having studied at least one foreign language causes one to perform better on this quiz.)