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1. A random sample of n = 64 is obtained from a population with standard deviation = 7, and the sample mean is computed to be = 42.

a. Construct a 95% confidence interval for the population mean.

b. Construct an 88% confidence interval for the population mean.

c. Test the null hypothesis versus the alternative hypothesis. Conduct the test with the critical value approach.

d. Test the null hypothesis 40 versus the alternative hypothesis 0.05. Conduct the test with the critical value approach.