Question

A data set includes data from student evaluations of courses. The summary statistics are n = 84, x = 3.35, s = 0.58. Use a 0.05 significance level to test the claim that the population of student course evaluations has a mean equal to 3.50. Assume that a sample random sample has been selected. a. Identify the null hypotheses and alternate hypotheses. addresses the original claim. Ho: H1: b. Find the test statistics equation and value. c. Find the P value for this hypothesis test. d. State the conclusion about Ho and H1. Why do we accept/reject Ho and accept/reject H1?

Answer 1

Solution :

Given that,

Population mean = = 3.50

Sample mean = = 3.35

Sample standard deviation = s = 0.58

Sample size = n = 84

Level of significance = = 0.05

This is a two tailed test.

a)

The null and alternative hypothesis is,

Ho: 3.50

Ha: 3.50

b)

The test statistics,

t = ( -   )/ (s/)

= ( 3.35 - 3.50 ) / ( 0.58 / 84)

= -2.37

c)

p-value = 0.0201

The p-value is p = 0.0201 < 0.05, it is concluded that the null hypothesis is rejected.

d)

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population of

student course evaluations has a mean equal to 3.50 . at 0.05 significance level.