A large random sample is used to construct a 99% confidence interval for the population mean . It is discovered that our hypothesis about the population mean, H lies outside this interval. Discuss whether each statement below is true or false. (a) Our hypothesis H is wrong. (b) A second confidence interval, constructed in the same way, has no more than a 1% chance of containing H. (c) If we took 10 samples and constructed one confidence interval for each sample mean, there is roughly a 90% chance that all 10 will contain , and 9% chance that only 9 of them contain , and less than a 1% chance that 8 or fewer contain . (d) If we constructed 1,000 confidence intervals in the same way, we'd expect 990 of them to contain the true population mean , whatever its value is.