I need the answer for this math question

Question

A simple random sample of 20 pages from a dictionary is obtained. The numbers of words defined on those pages are​ found, with the results n=20​, x=5.51 ​words, s=16.1 words. Given that this dictionary has 1455 pages with defined​ words, the claim that there are more than​ 70,000 defined words is equivalent to the claim that the mean number of words per page is greater than 48.1 words. Use a 0.01 significance level to test the claim that the mean number of words per page is greater than 48.1 words. What does the result suggest about the claim that there are more than​ 70,000 defined​ words? Identify the null and alternative​ hypotheses, test​ statistic, P-value, and state the final conclusion that addresses the original claim. Assume that the population is normally distributed. Determine the test statistic. ​(Round to two decimal places as​ needed.) Determine the P-value. ​(Round to three decimal places as​ needed.

Answer 1

H₀: The mean (μ) is less than or equal to 48.1 words per page.

H_A: The mean (μ) is greater than 48.1 words per page.

Since the sample size is less than 31 (n=20), use the t-test statistic.

t = (x -μ)/(σ/√n) = (5.51 - 48.1)/(16.1/√20)

≈ -11.8303273493 ≈ -11.83, rounded to 2 decimal places.

Use a t-score probability calculator with the degrees of freedom = n-1 = 20-1 = 19.

P(x>48.1) ≈ 0.000

We cannot reject the null hypothesis, since this is less than our significance level of 0.01

We cannot conclude that the mean number of entries per page is greater than 48.1; nor that the total number of entries in this dictionary exceeds 70,000.