9.33 Is the coin fair? In Example 4.3 (page 218), we learned that the South African statistician John Kerrich tossed a coin 10,000 times while imprisoned by the Germans during World War II. The coin came up heads 5067 times.

9.34 Goodness of fit to a standard Normal distribution. Computer software generated 500 random numbers that should look as if they are from the standard Normal distribution. They are categorized into five groups: (1) less than or equal to , (2) greater than and less than or equal to , (3) greater than and less than or equal to , (4) greater than and less than or equal to , and (5) greater than . The counts in the five groups are 140, 101, 43, 76, and 140, respectively. Find the probabilities for these five intervals using Table A. Then compute the expected number for each interval for a sample of 500. Finally, perform the goodness-of-fit test and summarize your results.

9.35 More on the goodness of fit to a standard Normal distribution. Refer to the previous exercise. Use software to generate your own sample of 500 standard Normal random variables and perform the goodness-of-fit test. Choose a different set of intervals than the ones used in the previous exercise.

9.36 Goodness of fit to a Poisson distribution. Refer to Example 5.30 (page 329) where a Poisson distribution is described as a model for the number of dropped calls on your cellphone per day. The mean number of calls is 2.1. In this setting, the probabilities for 0, 1, 2, and 3 or more dropped calls are 0.1225, 0.2572, 0.2700, and 0.3503, respectively. Suppose that you record the number of dropped calls per day for the next 100 days. Your observed counts of dropped calls are 11, 22, 28, and 39, respectively. Use a chi-square goodness of fit test to test the hypothesis that your calls are distributed according to this Poisson distribution.

9.37 More on the goodness of fit to a Poisson distribution. Refer to the previous exercise. Repeat the analysis using 10, 55, 22, and 53 as the observed counts. What do you conclude?