Question

One Sample t-test. A high school principal wants to know whether holding a review session affects final exam performance. Out of a large class, he selects a random sample of 9 students for the review session. Here are the results on the final exam: x bar= 28, s= 4, n= 9. In previous semesters, the final exam average was 24. Conduct a one-sample t-test to see if the average final exam score increase was real or if it was just chance variation. Use the following hypotheses:

H0: μ = 24 Ha: μ > 24

a. Compute the test statistic.

b. Find the p-value.

c. Determine whether to reject or fail to reject the null hypothesis (at alpha 0.05).

d. Write the conclusion, specifically tailored to the problem and hypotheses.

e. Would the determination be different if the alternative hypothesis was μ ≠ 24? Explain in detail.

Answer 1

a)

Test statistics

t = - / S / sqrt(n)

= 28 - 24 / 4 / sqrt(9)

= 3

b)

From The t table,

With test statistics of 3 and df = n -1 = 9 -1 = 8 ,

p-value = 0.0085

c)

Since p-value < 0.05 level, reject the null hypothesis.

d)

We conclude at 0.05 level that we have sufficient evidence to support the claim that average final exam

score increase was real or if it was just chance variation.

e)

If Ha: 24

Then p-value for two tailed test with t statistics of 3 and df of 8 is 0.0170

Since p-value < 0.05 level, we have sufficient evidence to reject the null hypothesis.