State whether each of the following statements is true or false:

(a) For a given number of population members and a given sample variance, the larger the number of sample members, the wider is a 95% confidence interval for the popula- tion mean.

(b) For a given number of population members and a given number of sample members, the larger the sample variance, the wider is a 95% confidence interval for the popula- tion mean.

(c) For a given number of sample members and a given sample variance, the larger the number of population members, the wider is a 95% confidence interval for the popula- tion mean. Justify your answer.

(d) For a given number of population members, a given number of sample members, and a given sample variance, a 95% confidence interval for the population mean is wider than a 90% confidence interval for the population mean.