Question

# 1. A statistics professor is examining if using the book in his class has any impact...

1. A statistics professor is examining if using the book in his class has any impact on student test scores. For a sample of 30 Statistics students who were required to buy and read the book for class, final semester grades were measured at the end of the semester. The mean final grade for this class was 87. If the mean final grade for all the previous classes (where students had not been required to use the book) was 83 with a standard deviation of 5, can the professor conclude that using the textbook changes students’ grades significantly? (Set the alpha level at .05) a. Complete all steps of the hypothesis test to test the null hypothesis.

Solution:

Given:

Sample size = n = 30

Sample mean = Population mean = Population standard deviation = Level of significance = 0.05

We have to test if using the textbook changes students’ grades significantly.

Step 1) State H0 and H1: Vs This is two tailed test, since hypothesis statement is non-directional and thus H1 is not equal to type.

Step 2) Test statistic:     Step 3) Find z critical values:

Since this is two tailed, we find : Area = Look in z table for area = 0.0250 or its closest area and find z value Area 0.0250 corresponds to -1.9 and 0.06

thus z critical value = -1.96

Since this is two tailed test, we have two z critical values: ( -1.96 , 1.96).

Step 4) Decision rule:

Reject null hypothesis ,if z  test statistic value < z critical value= -1.96 or  z  test statistic value> z critical value= 1.96, otherwise we fail to reject H0.

Since z  test statistic value = > z critical value= 1.96, we reject null hypothesis .

that means mean is different from 83..

Step 5) Conclusion:

At 0.05 level of significance ,professor have sufficient evidence to conclude that: using the textbook changes students’ grades significantly