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Can People Delay Death? A study indicates that elderly people are able to postpone death for a short time to reach an important occasion. The researchers \({ }^{10}\) studied deaths from natural causes among 1200 elderly people of Chinese descent in California during six months before and after the Harbor Moon Festival. Thirty-three deaths occurred in the week before the Chinese festival, compared with an estimated 50.82 deaths expected in that period. In the week following the festival, 70 deaths occurred, compared with an estimated 52. "The numbers are so significant that it would be unlikely to occur by chance," said one of the researchers. (a) Given the information in the problem, is the \(\chi^{2}\) statistic likely to be relatively large or relatively small? (b) Is the p-value likely to be relatively large or relatively small? (c) In the week before the festival, which is higher: the observed count or the expected count? What does this tell us about the ability of elderly people to delay death? (d) What is the contribution to the \(\chi^{2}\) -statistic for the week before the festival? (e) In the week after the festival, which is higher: the observed count or the expected count? What does this tell us about the ability of elderly people to delay death? (f) What is the contribution to the \(\chi^{2}\) -statistic for the week after the festival? (g) The researchers tell us that in a control group of elderly people in California who are not of Chinese descent, the same effect was not seen. Why did the researchers also include a control group?

Gender and Award Preference Example 2.6 on page 53 contains a two-way table showing preferences for an award (Academy Award, Nobel Prize, Olympic gold medal) by gender for the students sampled in StudentSurvey. The data are reproduced in Table \(7.28 .\) Test whether the data indicate there is some association between gender and preferred award. $$ \begin{array}{l|ccc|c} \hline & \text { Academy } & \text { Nobel } & \text { Olympic } & \text { Total } \\ \hline \text { Female } & 20 & 76 & 73 & 169 \\ \text { Male } & 11 & 73 & 109 & 193 \\ \hline \text { Total } & 31 & 149 & 182 & 362 \\ \hline \end{array} $$

Metal Tags on Penguins In Exercise 6.148 on page 445 we perform a test for the difference in the proportion of penguins who survive over a ten-year period, between penguins tagged with metal tags and those tagged with electronic tags. We are interested in testing whether the type of tag has an effect on penguin survival rate, this time using a chi-square test. In the study, 10 of the 50 metal-tagged penguins survived while 18 of the 50 electronic-tagged penguins survived. (a) Create a two-way table from the information given. (b) State the null and alternative hypotheses. (c) Give a table with the expected counts for each of the four categories. (d) Calculate the chi-square test statistic. (e) Determine the p-value and state the conclusion using a \(5 \%\) significance level.

Treatment for Cocaine Addiction Cocaine addiction is very hard to break. Even among addicts trying hard to break the addiction, relapse is common. (A relapse is when a person trying to break out of the addiction fails and uses cocaine again.) Data 4.7 on page 323 introduces a study investigating the effectiveness of two drugs, desipramine and lithium, in the treatment of cocaine addiction. The subjects in the six-week study were cocaine addicts seeking treatment. The 72 subjects were randomly assigned to one of three groups (desipramine, lithium, or a placebo, with 24 subjects in each group) and the study was double-blind. In Example 4.34 we test lithium vs placebo, and in Exercise 4.181 we test desipramine vs placebo. Now we are able to consider all three groups together and test whether relapse rate differs by drug. Ten of the subjects taking desipramine relapsed, 18 of those taking lithium relapsed, and 20 of those taking the placebo relapsed. (a) Create a two-way table of the data. (b) Find the expected counts. Is it appropriate to analyze the data with a chi-square test? (c) If it is appropriate to use a chi-square test, complete the test. Include hypotheses, and give the chi-square statistic, the p-value, and an informative conclusion. (d) If the results are significant, which drug is most effective? Can we conclude that the choice of treatment drug causes a change in the likelihood of a relapse?

Binge Drinking The American College Health Association - National College Health Assessment survey \(,{ }^{17}\) introduced on page 60 , was administered at 44 colleges and universities in Fall 2011 with more than 27,000 students participating in the survey. Students in the ACHA-NCHA survey were asked "Within the last two weeks, how many times have you had five or more drinks of alcohol at a sitting?" The results are given in Table 7.31 . Is there a significant difference in drinking habits depending on gender? Show all details of the test. If there is an association, use the observed and expected counts to give an informative conclusion in context. $$ \begin{array}{c|rr|r} \hline & \text { Male } & \text { Female } & \text { Total } \\ \hline 0 & 5,402 & 13,310 & 18,712 \\ 1-2 & 2,147 & 3,678 & 5,825 \\ 3-4 & 912 & 966 & 1,878 \\ 5+ & 495 & 358 & 853 \\ \hline \text { Total } & 8,956 & 18,312 & 27,268 \\ \hline \end{array} $$

Which Is More Important: Grades, Sports, or Popularity? 478 middle school (grades 4 to 6 ) students from three school districts in Michigan were asked whether good grades, athletic ability, or popularity was most important to them. \({ }^{18}\) The results are shown below, broken down by gender: $$ \begin{array}{lccc} \hline & \text { Grades } & \text { Sports } & \text { Popular } \\ \hline \text { Boy } & 117 & 60 & 50 \\ \text { Girl } & 130 & 30 & 91 \end{array} $$ (a) Do these data provide evidence that grades, sports, and popularity are not equally valued among middle school students in these school districts? State the null and alternative hypotheses, calculate a test statistic, find a p-value, and answer the question. (b) Do middle school boys and girls have different priorities regarding grades, sports, and popularity? State the null and alternative hypotheses, calculate a test statistic, find a p-value, and answer the question.

Favorite Skittles Flavor? Exercise 7.13 on page 518 discusses a sample of people choosing their favorite Skittles flavor by color (green, orange, purple, red, or yellow). A separate poll sampled 91 people, again asking them their favorite Skittles flavor, but rather than by color they asked by the actual flavor (lime, orange, grape, strawberry, and lemon, respectively). \(^{19}\) Table 7.32 shows the results from both polls. Does the way people choose their favorite Skittles type, by color or flavor, appear to be related to which type is chosen? (a) State the null and alternative hypotheses. (b) Give a table with the expected counts for each of the 10 cells. (c) Are the expected counts large enough for a chisquare test? (d) How many degrees of freedom do we have for this test? (e) Calculate the chi-square test statistic. (f) Determine the p-value. Do we find evidence that method of choice affects which is chosen? $$ \begin{array}{lcrccc} \hline & \begin{array}{l} \text { Green } \\ \text { (Lime) } \end{array} & \begin{array}{c} \text { Purple } \\ \text { Orange } \end{array} & \begin{array}{c} \text { Red } \\ \text { (Grape) } \end{array} & \begin{array}{c} \text { Yellow } \\ \text { (Strawberry) } \end{array} & \text { (Lemon) } \\ \hline \text { Color } & 18 & 9 & 15 & 13 & 11 \\ \text { Flavor } & 13 & 16 & 19 & 34 & 9 \end{array} $$

Handedness and Occupation Is the career someone chooses associated with being left- or right-handed? In one study \(^{20}\) a sample of Americans from a variety of professions were asked if they consider themselves left-handed, right-handed, or ambidextrous (equally skilled with the left and right hand). The results for five professions are shown in Table \(7.33 .\) (a) In this sample, what profession had the greatest proportion of left-handed people? What profession had the greatest proportion of right-handed people? (b) Test for an association between handedness and career for these five professions. State the null and alternative hypotheses, calculate the test statistic, and find the p-value. (c) What do you conclude at the \(5 \%\) significance level? What do you conclude at the \(1 \%\) significance level? $$ \begin{array}{l|rrr|r} \hline & \text { Right } & \text { Left } & \text { Ambidextrous } & \text { Total } \\ \hline \text { Psychiatrist } & 101 & 10 & 7 & 118 \\ \text { Architect } & 115 & 26 & 7 & 148 \\ \text { Orthopedic surgeon } & 121 & 5 & 6 & 132 \\ \text { Lawyer } & 83 & 16 & 6 & 105 \\ \text { Dentist } & 116 & 10 & 6 & 132 \\ \hline \text { Total } & 536 & 67 & 32 & 635 \\ \hline \end{array} $$