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statistics alive

Questions and Answers of Statistics Alive

11.89 Voting with 16 A recent survey of Austrian high school students asked whether it makes sense for 16-year-olds to be allowed to vote in the next parliamentary election.The following table shows
11.88 Likelihood-ratio chi-squared For testing independence, most software also reports another chi-squared statistic, called likelihood-ratio chi-squared. It equalsa. Show that G2 = X2 = 0 when each
11.87 Explaining Fisher’s exact test A pool of six candidates for three managerial positions includes three females and three males. Denote the three females by F1, F2, F3 and the three males by
11.86 Variability of chi-squared For the chi-squared distribution, the mean equals df and the standard deviation equals 221df2.a. Explain why, as a rough approximation, for a large df value, 95% of
11.85 What is df? The contingency table that follows has df = 4. Show that you can reconstruct the entire table by filling in the remaining cell counts based on the 4 cell counts shown. A B C D E
11.84 Degrees of freedom explained For testing independence in a contingency table of size r *c, the degrees of freedom (df) for the chi-squared distribution equal df = 1r - 12 * 1c - 12. They have
11.83 Standardized residuals for 2 : 2 tables The table that follows shows the standardized residuals in parentheses for GSS data about the statement, “Women should take care of running their homes
11.82 Multiple response variables Each subject in a sample of 100 men and 100 women is asked to indicate which of the following factors (one or more) are responsible for increases in crime committed
11.81 Normal and chi-squared with df • 1 When df = 1, the P-value from the chi-squared test of independence is the same as the P-value for the two-sided test comparing two proportions with the z
11.80 Statistical versus practical significance In any significance test, when the sample size is very large, we have not necessarily established an important result when we obtain statistical
11.79 True or false: Statistical but not practical significance Even when the sample conditional distributions in a contingency table are only slightly different, when the sample size is very large
11.78 True or false: Relative risk versus odds ratio Refer to a contingency table that cross-classifies subjects in two rows and two columns (labeled Success and Failure) and for which the odds ratio
11.77 True or false: Relative risk Interchanging the rows in a 2 * 2 contingency table has no effect on the value of the relative risk.
11.76 True or false: Group 1 becomes Group 2 Interchanging two rows or interchanging two columns in a contingency table has no effect on the value of the X2 statistic.
11.75 True or false: X2 • 0 The null hypothesis for the test of independence between two categorical variables is H0: X2 = 0 for the sample chi-squared statistic X2. (Hint:Do hypotheses refer to a
11.74 Colon cancer and race The State Center for Health Statistics for the North Carolina Division of Public Health released a report in 2010 that indicates that there are racial disparities in
11.73 Gun homicide in United States and Britain According to recent United Nations figures, the annual intentional homicide rate is 4.7 per 100,000 residents in the United States and 1.0 per 100,000
11.72 When is chi-squared not valid? Give an example of a contingency table for which the chi-squared test of independence should not be used.
11.71 Babies and gray hair A young child wonders what causes women to have babies. For each woman who lives on her block, she observes whether her hair is gray and whether she has young children,
11.70 Market price associated with factor cost? Whether the price of mango juice will rise is a categorical variable with categories (yes, no). Another categorical variable to consider is whether the
11.69 Another predictor of happiness? Go to sda.berkeley.edu/GSS and find a variable that is associated with happiness, other than variables used in this chapter. Use methods from this chapter to
11.68 Marital happiness decreasing? At sda.berkeley.edu/GSS, cross-tabulate HAPMAR with YEAR so you can see how conditional distributions on marital happiness in the GSS have changed since 1973.
11.67 Student data Refer to the FL Student Survey data file on the book’s website. Using software, create and analyze descriptively and inferentially the contingency table relating religiosity and
11.65 Clarity of diamonds Does the clarity of a diamond depend on its cut? Exercise 3.4 showed data, reproduced below, on the clarity (rated as internally flawless, IF, very very slightly included,
11.64 Botox side effects An advertisement for Botox Cosmetic by Allergan, Inc. for treating wrinkles appeared in several magazines. The back page of the ad showed the results of a randomized clinical
11.63 TV and aggression From a study described in Example 5 in the previous chapter, the proportion of males committing aggressive acts was 4 out of 45 for those who watched less than 1 hour of TV a
11.62 Education and religious beliefs When data from a recent GSS were used to form a 3 * 3 table that cross-tabulates highest degree 11 = less than high school, 2 = high school or junior college, 3
11.61 Happiness and sex A contingency table from the 2012 GSS relating happiness to number of sex partners in the previous year (0, 1, at least 2) had standardized residuals (called Z-statistic here)
11.60 Race and party ID The table shows data from an SPSS printout for some analyses of 2008 GSS data on race and party ID.a. Interpret the expected count for the first cell.b. Interpret the
11.59 Pesticides The following table, on the presence of pesticide residues in samples of organic and conventional food, was analyzed in Examples 2 and 3 in Chapter 3.a. Compute the relative risk and
11.58 Serious side effects In 2007, the FDA announced that the popular drug Zelnorm used to treat irritable bowel syndrome was withdrawn from the market, citing concerns about serious side effects.
11.57 Seat belt helps? The table refers to passengers in autos and light trucks involved in accidents in the state of Maine in a recent year.a. Use the difference of proportions to describe the
11.56 Women’s role A recent GSS presented the statement,“Women should take care of running their homes and leave running the country up to men,” and 14.8% of the male respondents agreed. Of the
11.55 Crossing peas When crossing round (R) and yellow (Y)peas with wrinkled (W) and green (G) peas, one can get any combination of color and appearance, denoted here as RY, RG, WY and WG, but traits
11.54 Aspirin and heart attacks for women A study in the New England Journal of Medicine compared cardiovascular events for treatments of low-dose aspirin or placebo among 39, 876 healthy female
11.53 Gender gap in employment? In a town, 7600 out of 8500 graduates are males. Out of 1750 graduate employees, 1620 are males.a. For these data, X2 = 23.24. What is its df value, and what is its
11.52 Gender gap? Exercise 11.1 showed a 2 * 3 table relating gender and political party identification, shown again here.The chi-squared statistic for these data equals 10.04 with a P-value of
11.51 Study hours and grades The following table shows data on study hours per week and the effect on grades, with expected cell counts given underneath the observed counts for 200 college students
11.50 Herbs and the common cold A recent randomized experiment of a multiherbal formula (Immumax) containing echinacea, garlic, ginseng, zinc, and vitamin C was found to improve cold symptoms in
11.49 Down and chi-squared For the data in the previous exercise, X2 = 114.4. Show all steps of the chi-squared test of independence.
11.48 Down syndrome diagnostic test The table shown, from Example 8 in Chapter 5, cross-tabulates whether a fetus has Down syndrome by whether the triple blood diagnostic test for Down syndrome is
11.47 Female participation in defense services? When people participating in recent surveys were asked if women should actively participate in defense services, about 91%of females and 91% of males
11.46 Proper meal timings enhance fitness? Refer to the previous exercise. Two months after the workshop, participants were asked whether shifting to proper meal timings was beneficial or not, with
11.45 Fitness workshop worthwhile? During a fitness workshop, participants were told about the importance of proper meal timings in staying fit. All 5 female participants changed their meal times as
11.44 AIDS and condom use Chatterjee et al. (1995, p. 132)described a study about the effect of condoms in reducing the spread of AIDS. This two-year Italian study followed heterosexual couples where
11.43 Claritin and nervousness An advertisement by Schering Corporation for the allergy drug Claritin mentioned that in a pediatric randomized clinical trial, symptoms of nervousness were shown by 4
11.42 Tea-tasting results Consider the tea-tasting experiment of Example 11 and Table 11.16. Consider the possible sample table in which all four of her predictions about the cups that had milk
11.41 Keeping old dogs mentally sharp In an experiment with beagles ages 7–11, the dogs attempted to learn how to find a treat under a certain black-colored block and then relearn that task with a
11.40 Ideology and political party Go to the GSS website sda.berkeley.edu/GSS/. Construct the 7 * 8 contingency table relating political ideology (POLVIEWS) and party identification (PARTYID) for the
11.39 Gender gap? The table in Exercise 11.1 on gender and party identification is shown again. The largest standardized residuals in absolute value were +2.98 for females who identified as Democrats
11.38 Happiness and marital status The screen shot from the GSS website shows standardized residuals (called Z-statistics) and cell counts for 2012 GSS data on happiness(the column) and marital
11.37 Recreation and happiness Exercise 11.32 showed the association between recreation and happiness. The table shown here gives the standardized residuals for those data in parentheses.a. Explain
11.36 Happiness and religious attendance The table shows MINITAB output for data from the 2008 GSS on happiness and frequency of attending religious services (1 = at most several times a year, 2 =
11.35 Standardized residuals for happiness and income The table displays the observed and expected cell counts and the standardized residuals for testing independence of happiness and family income,
11.34 Chi-squared versus measuring association For the table on recreation and happiness in Exercise 11.32, the chisquared statistic equals 168.78 (df = 4, P@value 6 0.0001).Explain the difference
11.33 Party ID and gender The table shows the 2012 GSS data on gender and political party identification from Exercise 11.1. (The row totals are slightly different from the second table in Exercise
11.32 Recreation and happiness The table shows data on indulgence in recreational activities and happiness for 398 individuals in a city.a. The chi-squared test of independence has X2 = 168.78.What
11.31 Risk of dying for teenagers According to summarized data from 1999 to 2006 accessed from the Centers of Disease Control and Prevention, the annual probability that a male teenager at age 19 is
11.30 Egg and cell derived vaccine When comparing the cell-derived flu vaccine mentioned in Example 9 to a more traditionally manufactured egg-derived vaccine, the following data were obtained.a.
11.29 Vioxx In September 2004, the pharmaceutical company Merck withdrew its blockbuster drug rofecoxib (a painkiller, better known under its brand name, Vioxx) from the worldwide market amid
11.28 Smelling and mortality A recent study (Pinto et al., Olfactory Dysfunction Predicts 5-Year Mortality in Older Adults. PLoS ONE 9(10):e107541, 2014)mentions that anosmic (those with almost no
11.27 Gender and dominant hand usage The following table cross-tabulates dominant hand usage by gender for 200 individuals. Find and interpret a measure of association, treating hand usage as the
11.26 Smoking and alcohol The table refers to a survey of senior high school students in Dayton, Ohio. It cross-tabulates whether a student had ever smoked cigarettes and whether a student had ever
11.25 Death penalty associations Table 11.10, summarized again here, showed the associations between death penalty opinion and gender or race.a. True or false: The table with the larger X2 statistic
11.24 Democrat, race, and gender The two tables show 2012 GSS data on whether someone is identified as Democrat, by race and by gender.a. Find the difference of proportions between blacks and whites
11.23 Checking a roulette wheel Karl Pearson devised the chi-squared goodness-of-fit test partly to analyze data from an experiment to analyze whether a particular roulette wheel in Monte Carlo was
11.22 Footfall by quarters Based on a random sample of 1098 customers at a grocery store, the table shows how many arrived in the first, second, third, and fourth quarter of the year. Is there
11.21 Testing a genetic theory In an experiment on chlorophyll inheritance in corn, for 1,103 seedlings of self-fertilized heterozygous green plants, 854 seedlings were green and 249 were yellow.
11.20 What is independent of happiness? Refer to Exercises 11.6 and 11.7. For the variables that you thought might be independent,a. At the GSS website, conduct all five steps of the chi-squared
11.19 Severity of fever after flu shot The study mentioned in Example 5 also looked at the severity of fever (rated as mild, moderate or severe) for all subjects who developed one after receiving a
11.18 z test for anxiety study Refer to the previous exercise.The printout from MINITAB reports Test for difference = 0 (vs not = 0):Z = 2.12 P-Value = 0.033a. Define population proportions p1 and p2
11.17 Cognitive behavioral therapy and anxiety A study used 1496 patients suffering from low levels of anxiety. The study randomly assigned each subject to a cognitive behavioral therapy (CBT)
11.16 Primary food choice of alligators For alligators caught in two Florida lakes, the following table shows their primary food choice. The four food categories refer to fish, invertebrates(such as
11.15 Help the environment In 2010 the GSS asked whether a subject was willing to accept cuts in the standard of living to help the environment (GRNSOL), with categories(vw = very willing, fw =
11.14 Smoking and alcohol Refer to the previous exercise.A similar table relates cigarette use to alcohol use.The MINITAB output for the chi-squared test follows.a. True or false: If we use cigarette
11.13 Cigarettes and marijuana The table on the following page refers to a survey2 in which senior high school students in Dayton, Ohio, were randomly sampled. It cross-tabulates whether a student
11.12 First and second free throw independent? In pro basketball games during 1980–1982, when Larry Bird of the Boston Celtics made his first free throw, 251 out of 285 times he made the second
11.11 Marital happiness and income In Exercise 11.5 when you used the GSS to download a 3 * 3 table for family income and marital happiness in 2012, you should have obtained results similar to the
11.10 What gives a P@value • 0.01? How large an X2 test statistic value provides a P-value of 0.01 for testing independence for the following table dimensions?a. 2 * 2b. 2 * 3c. 3 * 5d. 4 * 5e. 5 *
11.9 Happiness and gender For the 2 * 3 table on gender and happiness in Exercise 11.4 (shown below), software tells us that X2 = 1.04 and the P@value = 0.59.a. State the null and alternative
11.8 Lung cancer and smoking In a study conducted by a pharmaceutical company, 605 out of 790 smokers and 122 out of 434 nonsmokers were diagnosed with lung cancer.a. Construct a 2 * 2 contingency
11.7 Sample evidence about independence Refer to the previous exercise. Go to the GSS website and construct a table relating happiness (HAPPY) to the variable you chose (AFTERLIF, FINRELA, HEALTH,
11.6 What is independent of happiness? Which one of the following variables would you think most likely to be independent of happiness: belief in an afterlife, family income, quality of health,
11.5 Marital happiness and income In the GSS, subjects who were married were asked about the happiness of their marriage, the variable coded as HAPMAR.a. Go to the GSS website sda.berkeley.edu/GSS/,
11.4 Happiness and gender The contingency table shown relates happiness and gender for the 2012 GSS.a. Identify the response variable and the explanatory variable.b. Construct a table or graph
11.3 Williams College admission Data from 2013 posted on the Williams College website shows that of all 3,195 males applying, 18.2% were admitted, and of all 3,658 females applying, 16.9% were
11.2 Beliefs of new employees Every year, a large-scale poll of new employees conducted by the human resources management department at a consulting firm asks their opinions on a variety of issues.
11.1 Gender gap in politics? In the United States, is there a gender gap in political beliefs? That is, do women and men tend to differ in their political thinking and voting behavior? The table
10.92 More knee pain Refer to the previous exercise.Compare the placebo to the debridement group using a significance test. State the assumptions and explain how to interpret the P-value.
10.91 Surgery versus placebo for knee pain Refer to Example 10 on whether arthroscopic surgery is better than placebo. The following table shows the pain scores one year after surgery. Using software
10.89 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
10.88 Car bumper damage An automobile company compares two types of front bumpers for its new model by driving sample cars into a concrete wall at 20 miles per hour. The response is the amount of
10.87 Parental support and household type A recent study interviewed youths with a battery of questions that provides a summary measure of perceived parental support.This measure had sample means of
10.86 How often do you feel sad? A recent General Social Survey asked, “How many days in the past seven days have you felt sad?” Software comparing results for men and women who responded showed
10.93 Anorexia again Refer to Exercise 10.89, comparing mean weight changes in anorexic girls for cognitive behavioral therapy and a control group. The MINITAB output shows results of doing analyses
10.94 Breast-feeding helps IQ? A Danish study of individuals born at a Copenhagen hospital between 1959 and 1961 reported higher mean IQ scores for adults who were breast-fed for longer lengths of
10.95 Australian cell phone use In Western Australia, handheld cell phone use while driving has been banned since 2001, but hands-free devices are legal. A study (published in the British Medical
10.96 Improving employee evaluations Each of a random sample of 10 customer service representatives from a large department store chain answers a questionnaire about how they respond to various
10.97 Which tire is better? A tire manufacturer believes that a new tire it is introducing (Brand A) will have longer wear than the comparable tire (Brand B) sold by its main competitor.To get
10.98 Effect of alcoholic parents A study14 compared personality characteristics between 49 children of alcoholics and a control group of 49 children of nonalcoholics who were matched on age and

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