8.85 Too many errors. Refer to the previous exercise. The chance that each of the six intervals that you calculated includes the true proportion for that genre is approximately 95%. In other words, the chance that your interval misses the true value is approximately 5%.
(a) Explain why the chance that at least one of your intervals does not contain the true value of the parameter is greater than 5%.
(b) One way to deal with this problem is to adjust the confidence level for each interval so that the overall probability of at least one miss is 5%. One simple way to do this is to use a Bonferroni procedure. Here is the basic idea: You have an error budget of 5% and you choose to spend it equally on six intervals. Each interval has a budget of 0.05/6 = 0.008. So, each confidence interval should have a 0.8% chance of missing the true value. In other words, the confidence level for each interval should be 1 − 0.008 = 0.992. Use Table A to find the value of z* for a large-sample confidence interval for a single proportion corresponding to 99.2% confidence.
(c) Calculate the six confidence intervals using the Bonferroni procedure.