. An independent random sample of size n = 12 is selected from an approximately Normal population with standard deviation = 2.3. A hypothesis test on the population mean is conducted such that the alternative hypothesis is Ha : 6= 0.

(a) Briefly explain why the sampling distribution of all sample means, x, calculated from samples of size n = 12 is approximately Normal.

(b) Calculate the p-value if the z test statistic is z = 1.25. Round your answer to three decimal places. Be sure to include the Microsoft Excel or graphing calculator commands that you used.

(c) Do we reject the null hypothesis, H0 : = 0, at the 2% significance level? Why or why not?

(d) (2 points) What is the largest sample size needed to estimate the true mean to within 2 with 98% confidence? In other words, what should n be so that the margin of error of the 98% confidence interval is 2? Keep in mind that n must be a whole number. (Note that the critical z-score that you use must be rounded to at least two decimal places.)