Answer all questions with explanation

Suppose the random variable has Normal distribution with unknown expected value of , i.e., = (), and unknown standard deviation = (). Given the sample above,

a. [2 points] estimate using the sample mean b. [2 points] estimate using the sample standard deviation

c. [2 points] construct a 95% confidence interval for

d. [2 points] construct a 90% confidence interval for Now let's test the hypotheses about . The null hypothesis is stated as 0: = 130.

e. [2 points] Suppose the alternative is 1: 130, can you reject 0 at 5% significance level?

f. [2 points] Suppose the alternative is 1: < 130, can you reject 0 at 5% significance level?