Question

A data set includes data from student evaluations of courses. The summary statistics are n equals=92, x equals=4.09​, s equals=0.62. Use a 0.05 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?

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.

? H0. 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.

Answer 1

The null and alternative hypothesis are

H0: = 4.25

Ha: 4.25

Test statistics

t = ​​​​​​ - / ( S / sqrt(n) )

= 4.09 - 4.25 / (0.62 / sqrt(92) )

= -2.48

From T table,

With test statistics -2.48 and df of 91,

p-value (Two tailed) = 0.015

Since p-value < 0.05 level, we have sufficient evidence to reject H0.

We conclude at 0.05 level that we have sufficient evidence to support the claim.