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 describe and make inferences about the association, in a one-page report.

When looking at a collection of numbers, such as population sizes, the figures on tax returns or the charges on a credit card, one may think that the leading digit of the number is equally likely to be any of the numbers from 1 to 9. However, such data sets often show a distribution for the leading digit that is quite different from uniform and is described by Benford's Law. This law stipulates that the probability for the leading digit to be 1 is 30.1%, whereas the probability of the leading digit to be 9 is only 4.6% instead of a unifom 1/9 = 11.1% probability for each. The following table shows the distribution of the leading digit of the last 130 transactions on the credit ca rd of one of the authors. The raw data file is available for download on the book's website.

Find the expected counts, assuming the leading digits for the transactions follow Benford's Law.

Does the clarity of a diamond depend on its cut? One analysis showed data, reproduced below, on the clarity (rated as internally flawless, IF, very very slightly included, VVS, very slightly included, VS , slightly included, SI and included, I) for the two lowest ratings for cut, which are "good" and "fair.

Use the Permutation Test of Independence web app accessible from the book's website to enter the contingency table and replicate the results from part c.

Does the clarity of a diamond depend on its cut? One analysis showed data, reproduced below, on the clarity (rated as internally flawless, IF, very very slightly included, VVS, very slightly included, VS , slightly included, SI and included, I) for the two lowest ratings for cut, which are "good" and "fair.

Of 10,000 random permutations, 9,908 resulted in an $X^2$ value as large or larger than the one observed. Find the (approximate) permutation P-value and interpret.

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 trial to compare 405 people receiving Botox injections to 130 people receiving placebo in terms of the frequency of various side effects. The side effect of pain in the face was reported by 9 people receiving Botox and Opeople receiving placebo. Use software (or a web app) to conduct a two-sided test of the hypothesis that the probability of this side effect is the same for each group. Report all steps of the test and interpret results.

Does the clarity of a diamond depend on its cut? One analysis showed data, reproduced below, on the clarity (rated as internally flawless, IF, very very slightly included, VVS, very slightly included, VS , slightly included, SI and included, I) for the two lowest ratings for cut, which are "good" and "fair.

Can you use the chi-squared distribution to find a P-value? Why or why not?

From a one study, the proportion of males committing aggressive acts was 4 out of 45 for those who watched less than 1 hour of TV a day and 117 out of 315 for those who watched at least 1 hour per day. MINITAB reports the printout shown for conducting Fisher's exact test (two-sided) for these data.

Report the P-value that software reports and interpret in the context of this study.

Data on TV watching and aggression

Rows : TV Column : aggression

Does the clarity of a diamond depend on its cut? One analysis showed data, reproduced below, on the clarity (rated as internally flawless, IF, very very slightly included, VVS, very slightly included, VS , slightly included, SI and included, I) for the two lowest ratings for cut, which are "good" and "fair.

Verify, using software, that $X^2$ = 0.267 for this table. The (raw) data are available on the book's website as Diamonds.csv.

From a one study, the proportion of males committing aggressive acts was 4 out of 45 for those who watched less than 1 hour of TV a day and 117 out of 315 for those who watched at least 1 hour per day. MINITAB reports the printout shown for conducting Fisher's exact test (two-sided) for these data.

State hypotheses for the test, defining the notation.

Data on TV watching and aggression

Rows : TV Column : aggression

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, region of the country in which you live, satisfaction with job? Explain the basis of your reasoning.

When data from a recent GSS were used to form a 3 x 3 table that cross-tabulates highest degree (1 = less than high school, 2 = high school or junior college, 3 = bachelor or graduate) with religious beliefs (F = fundamentalist, M = moderate, L = liberal), the three largest standardized residuals were: 6.8 for the cell (3, F), 6.3 for the cell (3, L), and 4.5 for the cell (1, F). Summarize how to interpret these three standardized residuals.

The table shows data from an SPSS printout for some analyses of 2008 GSS data on race and party ID.

How would you summarize to someone who has never studied statistics what you learn from the standardized residuals given in the four comer cells on this printout?

The table shows data from an SPSS printout for some analyses of 2008 GSS data on race and party ID.

Interpret the standardized residual of 12.5 for the first cell (SPSS calls it an adjusted residual).

The table shows data from an SPSS printout for some analyses of 2008 GSS data on race and party ID.

Interpret the expected count for the first cell.