Landon is doing some simulations to see how well the simulated coverage rate compares to the nominal 95% coverage rate in various situations. For each situation Landon simulates 10,000 samples and computes the coverage rate.
a) How high or low must the simulated coverage rate be for Landon to suspect that the true coverage rate is not 95%? Assume our usual threshold of significance, α = 0.05.
b) Do we have evidence that any of the 95% confidence interval simulations performed in this chapter do not have coverage rates of 95%?
c) Landon realizes that his methods are only approximations. How high or low must the simulated coverage rate be for Landon to suspect that the true coverage rate is not between 94% and 96%?
d) Do we have evidence that any of the 95% confidence interval simulations performed in this chapter do not have coverage rates between 94% and 96%?