40 married couples without children are asked to report the number of times per year they initiate a date night. The men report initiating an average of 9.3 date nights with a standard deviation of 4....

40 married couples without children are asked to report the number of times per year they initiate a date night. The men report initiating an average of 9.3 date nights with a standard deviation of 4. Is there significant evidence to conclude that married men without children initiate date night more than 8 times per year at the 0.01 significance level? Note that there's evidence that this distribution is skewed.


What are the hypotheses?

What distribution does the test statistic follow?

What is the value of the test statistic? Round to two decimal places.

4.8 More posterior predictive checks: Let 4 and 5 be the average num- ber of children of men in their 30s with and without bachelor’s degrees, respectively. a) Using a Poisson sampling model, a gamma(2.1) prior for each 6 and the data in the files menchild30bach.dat and menchild30nobach.dat, obtain 5,000 samples of ¥4 and Yj from the posterior predictive dis- tribution of the two samples. Plot the Monte Carlo approximations to these two posterior predictive distributions. b) Find 95% quantile-based posterior confidence intervals for 65 —64 and Yp—Ya. Describe in words the differences between the two populations using these quantities and the plots in a), along with any other results that may be of interest to you. Obtain the empirical distribution of the data in group B. Compare this to the Poisson distribution with mean # = 1.4. Do you think the Poisson model is a good fit? Why or why not? For each of the 5,000 f -values you sampled, sample ny; = 218 Poisson random variables and count the number of 0s and the number of 1s in each of the 5.000 simulated datasets. You should now have two sequences of length 5,000 each, one sequence counting the number of people having zero children for each of the 5,000 posterior predictive datasets, the other counting the number of people with one child. Plot the two sequences against one another (one on the z-axis, one on the y-axis). Add to the plot a point marking how many people in the observed dataset had zero children and one child. Using this plot, describe the adequacy of the Poisson model. ¢ d)