Question

5. (7) To see if female math majors study harder than males, we collected a random sample of study hours per day from math majors. Assume all variables have normal distributions, answer the questions based on the provided outputs using correct statistical technique.

                                                                 

         Paired Samples Test

	Paired Differences mean	Std. Dev.	Std. Error	t	Sig. (2-tailed)
female– male	.4	.750	.250	1.98	.058

Group Statistics
	gender	N	Mean	Std. Deviation	Std. Error Mean
hours	male	22	1.0985	.416654	.088831
	female	24	2.4996	.334813	.068343

        Independent Samples Test

	Levene's Test for Equality of Variances		t-test for Equality of Means
	F	Sig.	t	Sig. (2-tailed)
Equal variances assumed	.043	.2373	-1.613	0.0924
Eequal variances not assumed			-1.721	0.0881

                                                              

1. Is it a paired samples t test or independent samples t test?

2. Set up Ho and Ha to prove that females study harder:

         

3. What is the value of t and P-value for the test in part (b)?

4. Will H_o be rejected at 5% level of significance?

5. What is your final conclusion (for the hypothesis test)?

Answer 1

a). It is an independent samples t-test

Let the subscript 1 denote males and 2 denotes females. Then

b).

c). The test statistic is :

Where is the pooled variance.

hours	male	22	1.0985	.416654	0.08831
	female	24	2.4996	.334813	.068343

We shall take the summary statistic from the tables

c). The p-value of the test is p=0,0000.

d). Since the p-value <0.05, we reject the null hypothesis.

e). It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that population the mean study hours of females is more than the male study hours.