Question

For each of the dependent means t-tests below:

1) State the null and alternative hypotheses

2) Set the criteria for a decision (i.e. state alpha, one- or two-tailed test, degrees of freedom and the cutoff score(s)

3) Compute: The mean of the difference scores, the sum of squares, the estimated population variance of difference scores, the variance of the distribution of means of difference scores and the standard deviation of the distribution of means of difference scores (show all work)

4) Compute the test statistic (t_obt)

5) Decide whether to retain/reject the null hypothesis

6) State your conclusion in APA format (make sure to report the type of test used, the I.V., the D.V., whether it was significant or not, your test statistic (t), and the means of time 1 and time 2; see the lecture slides for examples)

Problem 2:

Brett wants to know if living in the south changes how much people like country music. To test this hypothesis (α = .01), he has 6 students rate how much they like country music on a scale from 0-10 (0 = do not like, 10 = like a lot) at the beginning of their freshman year (Time 1) and then again at the end of their senior year (Time 2). Carry out a hypothesis test to see if living in the south changes student’s opinions of country music.

Student	Time 1	Time 2
1	7	7
2	5	4
3	6	8
4	3	5
5	6	7
6	4	3

Answer 1

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μD= 0

Ha: μD ≠ 0

This corresponds to a two-tailed test, for which a t-test for two paired samples be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.01, and the degrees of freedom are df=5.

Hence, it is found that the critical value for this two-tailed test is tc =4.032, for α=0.01 and df=5.

The rejection region for this two-tailed test is R={t:∣t∣>4.032}.

(3) Test Statistics

The t-statistic is computed as shown in the following formula:

(4) Decision about the null hypothesis

Since it is observed that ∣t∣=0.889≤tc=4.032, it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p=0.415, and since p=0.415≥0.01, it is concluded that the null hypothesis is not rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean μ1 is different than μ2 , at the 0.01 significance level.