Question

The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures students study habits and attitude toward school. Scores range from 0 to 200. The mean score for college students is about 95, and the standard deviation is about 20. A teachers who suspects that older students have better attidues towards school gives SSHA to 20 students who are at least 30 years of age. There mean scores is 106.

a) What is the z-score for this hypothesis test?

b) what is the P-value for this test?

c) What is the correct conclusion for this hypothesis test?

There is evidence at the .05 level that older students are more motivated than younger students.

There is not evidence at the .05 level that older students are less motivated than younger students.

There is not evidence at the .05 level that older students are more motivated than younger students.

There is evidence at the .05 level that older students are less motivated than younger students.

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 95
Alternative Hypothesis, Ha: μ > 95

Rejection Region
This is right tailed test, for α = 0.05
Critical value of z is 1.645.
Hence reject H0 if z > 1.645

Test statistic,
z = (xbar - mu)/(sigma/sqrt(n))
z = (106 - 95)/(20/sqrt(20))
z = 2.46

P-value Approach
P-value = 0.0069
As P-value < 0.05, reject the null hypothesis.

There is evidence at the .05 level that older students are more motivated than younger students.