A simple random sample of pages from Merriam-Webster’s Collegiate Dictionary,

A simple random sample of pages from Merriam-Webster’s Collegiate Dictionary, 11th edition, is obtained. With the number of words defined in a sample of 11 pages, a sample average is x ̅= 53.30, and a sample standard deviation is s = 15.6564. Given that this dictionary has 1459 pages with defined words, the claim that there are more than 70,000 defined words is the same as the claim that the mean number of defined words on a page is greater than 48.0. Using a 0.05 significance level, we wish to test the claim that the mean number of defined words on a page is greater than 48.0. A normal probability plot reveals that the population of number of defined words on a page is approximately normally distributed.
State the null and alternative hypotheses.

H0 (null hypothesis):
H1 (alternative hypothesis):

Select the distribution (Z-distribution or t-distribution) to use. Explain briefly why you selected it.

Assuming that they wish to test the claim at  (level of significance) = 0.05, determine the rejection and non-rejection regions based on your hypotheses in a). State the critical value.

Calculate the value of the test statistic.

Based on the results of c) and d), what do they suggest about the claim that there are more than 70,000 defined words in the dictionary? Explain your conclusion in words.