Question

12)(Reject) (sufficient) (is)

A data set includes data from student evaluations of courses. The summary statistics are n = 84, x = 4.18, S = 0.63. Use a 0.10 significance level to test the claim that the population of student course evaluations has a mean equal to 4.25. Assume that a simple random sample has been selected. Identify the null and alternative hypotheses, test statistic, P-value, and state the final conclusion that addresses the original claim. What are the null and alternative hypotheses? O A. Ho: = 4.25 H:<4.25 | 0 C. Ho H = 4.25 H:+4.25 O B. Ho: = 4.25 H:> 4.25 OD. Ho: +4.25 He: p=4.25 Determine the test statistic. (Round to two decimal places as needed.) Determine the P-value. (Round to three decimal places as needed.) State the final conclusion that addresses the original claim. Ho. There is evidence to conclude that the original claim that the mean of the population of student course evaluations is equal to 4.25 correct

(Fail to reject) (Not sufficient) (is not)

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :  $\mu$ = 4.25

H_a : $\mu$ $\neq$ 4.25

Test statistic (t)

= ($\bar x$ - $\mu$) / s / $\sqrt$n

= (4.18 - 4.25) /0.63 / $\sqrt$84

Test statistic = -1.018

2 * P(z < -1.018) = 2 * 0.1543

P-value = 0.3086‬

$\alpha$ = 0.10

P-value > $\alpha$

Fail to reject H₀.There is no sufficient evidence to conclude the original claim that the mean of the population of student course evaluations is equal to 4.25 mean.