a. A sample of size n = 100 produced the sample mean of X = 59. Assuming the population standard deviation = 4, compute a 95% confidence interval for the population mean .

b. A sample of size n = 100 produced the sample mean of X = 59. Assuming the population standard deviation = 4, compute a 90% confidence interval for the population mean .

c. A sample of size n = 100 produced the sample mean of X = 59. Assuming the population standard deviation = 4, compute a 99% confidence interval for the population mean .

d. A sample of size n = 25 produced the sample mean of X = 59. Assuming the population standard deviation = 4, compute a 95% confidence interval for the population mean .

e. A sample of size n = 400 produced the sample mean of X = 59. Assuming the population standard deviation = 4, compute a 95% confidence interval for the population mean .

f. A sample of size n = 100 produced the sample mean of X = 59. Assuming the population standard deviation = 1, compute a 95% confidence interval for the population mean .

g. A sample of size n = 100 produced the sample mean of X = 59. Assuming the population standard deviation = 16, compute a 95% confidence interval for the population mean .

h. Compare the confidence intervals found in part a with that in each of the other previous parts of this problem (b, c, . . ., g). Explain why one is wider than the other.

Using R