Question

a) A researcher was interested in whether the female students who enrolled in her stats course were more interested in the topic than the males. The researcher obtained a random sample of 8 male and 8 female students and gathered their scores on an Interest in Statistical Topics (IST) Survey.

Girls’ IST scores: 21, 37, 22, 20, 22, 20, 22, 21

Boys’ IST scores: 20, 20, 20, 21, 21, 20, 23, 21

Test the researcher’s hypothesis using α =.05

Answer 1

here, we will do independent 2 sample t test.

a).hypothesis:-

where, is the population mean score of girl's and   is the population mean score of boy's.

b).necessary calculation for mean and sd be:-

girl's score()	boy's score ()
21	20	4.515625	0.5625
37	20	192.5156	0.5625
22	20	1.265625	0.5625
20	21	9.765625	0.0625
22	21	1.265625	0.0625
20	20	9.765625	0.5625
22	23	1.265625	5.0625
21	21	4.515625	0.0625
sum= 185	sum=166	sum=224.9	sum=7.5

the test statistic be:-

the degrees of freedom be:-

= 7

critical value of t for 95% confidence interval 1 sided:-

[ from t distribution table, for df = 7, alpha= 0.05, one tailed test]

decision:-

so, we do not have enough evidence to reject our null hypothesis.

conclusion:-

WE, FAIL TO REJECT H₀

there is not enough evidence to support the claim that the female students who enrolled in her stats course were more interested in the topic than the males at 0.05 level of significance.

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