Question

1. In the Excel data file, the tab labeled Question 1 contains data on the number of times boys and girls raise their hands in class. Conduct the t-test: Two-Sample Assuming Equal Variances.
2. Males 9,8,4,9,3,8,10,8,9,10,7,6,12
3. Females 3,5,1,2,6,4,3,6,7,9,7,3,7,6,8,8

a. What is the null hypothesis?

b. What is the research hypothesis?

c. Why run a Two-Sample Assuming Equal Variances t-test?

d. Interpret the findings. What are the results of the hypothesis test? Can you reject the null hypothesis?

Answer 1

Assume that both the populations of males and females who raise their hands are distributed normally.

a) Null hypothesis

b) Research hypothesis

c) We run a two-sample t-test assuming equal variances because we assume that there is not much spread among the students in a class raising their hands. A t-test is appropriate because the male and female populations are independent of each other and homoscedastic.

d) we can estimate the population variance from the sample pooled variance since we assume that the populations are homoscedastic.

, under the null hypothesis. Here, S= pooled variance

	9	3	1.159763	5.347656
	8	5	0.005917	0.097656
	4	1	15.39053	18.59766
	9	2	1.159763	10.97266
	3	6	24.23669	0.472656
	8	4	0.005917	1.722656
	10	3	4.313609	5.347656
	8	6	0.005917	0.472656
	9	7	1.159763	2.847656
	10	9	4.313609	13.59766
	7	7	0.852071	2.847656
	6	3	3.698225	5.347656
	12	7	16.6213	2.847656
		6		0.472656
		8		7.222656
		8		7.222656
total	103	85	72.92308	85.4375
average	7.923077	5.3125

so,

and and

Hence,

To test the hypothesis, test statistic is:

From sample information, T= 7.731436

Critical value = =

We reject the null hypothesis at 5% level of significance, since |T| > critical value.

So,we conclude that there is a difference in the number of males and females who raise their hand in class.