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 the 95% confidence interval for the population mean.
b. For a given number of population members and a given number of sample members, the larger the sample variance, the wider the 95% confidence interval for the population mean.
c. For a given number of sample members and a given sample variance, the larger the number of population members, the wider the 95% confidence interval for the population 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.