1. Suppose that you are testing the hypotheses H0: m = 16 vs. HA: m 6 16. A sample of size 25 results in a sample mean of 16.5 and a standard deviation of 2.0.
a) What is the standard error of the mean?
b) What is the critical value of t* for a 90% confidence interval?
c) Construct a 90% confidence interval for m.
d) Based on the confidence interval, at a = 0.05 can you reject H0? Explain.
2. Suppose that you are testing the hypotheses H0: m = 80 vs. HA: m Z 80. A sample of size 61 results in a sample mean of 75 and a standard deviation of 1.5.
a) What is the standard error of the mean?
b) What is the critical value of t* for a 95% confidence in- terval?
c) Construct a 95% confidence interval for m.
d) Based on the confidence interval, at a = 0.05 can you reject H0? Explain.