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 you make an error and 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 = 0.0083. So each confidence interval should have a 0.83% chance of missing the true value.

In other words, the confidence level for each interval should be 1 − 0.0083 = 0.9917. Use Table A to find the value of z for a large-sample confidence interval for a single proportion corresponding to 99.17% confidence.

(c) Calculate the six confidence intervals using the Bonferroni procedure.