I. Suppose you have 30 observations from a normal distribution. The sample mean is 15 and the variance of X is 25. You want to test whether the sample mean is significantly different from 13.

A.) Write down the null and alternative hypotheses

B.) Calculate your Z statistic.

C.) Can you reject the null hypothesis at the 5% significance level? (Report your critical value)

D.) Can you reject the null hypothesis at the 1% significance level? (Report your critical value)

E.) Report the 95% confidence interval for your sample.

II. You have 30 observations from a normal distribution. The sample mean is 15 and the variance of X is 25. You want to test whether your sample is significantly greater than 13.

A.) Write down the null and alternative hypotheses

B.) Calculate your Z statistic.

C.) Can you reject the null hypothesis at the 5% significance level? (Report your critical value)

D.) Can you reject the null hypothesis at the 1% significance level? (Report your critical value)

III. Assume that b is a constant, X and Y are variables and Z=bXY. Use probability limit rules to break plim(Z) into its individual components. As always, show your work.

A.) Write down the null and alternative hypotheses

B.) Calculate your Z statistic.

C.) Can you reject the null hypothesis at the 5% significance level? (Report your critical value)

D.) Can you reject the null hypothesis at the 1% significance level? (Report your critical value)

E.) Report the 95% confidence interval for your sample.

II. You have 30 observations from a normal distribution. The sample mean is 15 and the variance of X is 25. You want to test whether your sample is significantly greater than 13.

A.) Write down the null and alternative hypotheses

B.) Calculate your Z statistic.

C.) Can you reject the null hypothesis at the 5% significance level? (Report your critical value)

D.) Can you reject the null hypothesis at the 1% significance level? (Report your critical value)

III. Assume that b is a constant, X and Y are variables and Z=bXY. Use probability limit rules to break plim(Z) into its individual components. As always, show your work.

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