Please use the following information to answer questions 7a-7e:

The librarian at the local elementary school claims that, on average, the books in the library are more than 20 years old. To test this claim, a student takes a sample ofn= 30 books and records the publication date for each. The sample produces an average ofx = 23.8 years with a variance ofs²= 67.5.

Determine whether the average age of the library books is significantly greater than 20 years.Use a one-tailed test with= .01.

7a. Which of the following correctly represents the null and alternative hypothesis for the mentioned sample ofn= 30 (MUST SHOW WORK FOR THIS PROBLEM)?

Ho: 20 H_1:< 20

Ho: 20 H_1:> 20

Ho:> 20 H_1: 20

Ho:= 20

H_1: 20

7b.Which of the followingrepresents the critical region for this mentioned sample(MUST SHOW WORK FOR THIS PROBLEM)?

t=2.462

t=2.462

t=2.756

t=2.756

7c.Compute the test statistic(t-observed)for the mentioned sample(MUST SHOW WORK FOR THIS PROBLEM).

7d.Based on the calculated test statistic,would you reject the null hypothesis established in question 7a(MUST SHOW WORK FOR THIS PROBLEM)?

yes

no

7e.Based on the previously conducted steps,we canconclude (MUST SHOW WORK FOR THIS PROBLEM):

The average age of the library books is significantly less than20years.

The average age of the library books is significantly greater than 20 years.

The average age of the library books is significantly differentthan20years.

The average age of the library books is approximately20years.