Question

The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures the motivation, attitude toward school, and study habits of students. Scores range from 0 to 200. A selective private college gives the SSHA to an SRS of both male and female first-year students. The data for the women are as follows: 154 109 137 115 152 140 154 178 101 103 126 126 137 165 165 129 200 148 Here are the scores of the men: 108 140 114 91 180 115 126 92 169 146 109 132 75 88 113 151 70 115 187 104 Most studies have found that the mean SSHA score for men is lower than the mean score in a comparable group of women. Is this true for first-year students at this college? Use a 1% significance level

(a) Hypotheses and results:

(b) Draw a picture and label p-value and horizontal axis:

(c) Draw a conclusion. Don’t just accept or reject. Say what it means in terms of this problem.

Answer 1

We are here comparing two independent samples. And we have not yet been provided with population variances. So we are going to use t-dist to carry the test for the difference of population means.

We want to test if mean SSHA score for men is lower than the mean score in a comparable group of women. Therefore it means or  

This is a one sided test. Also we will assume that they have same population variances

Sr. No.	Women (X1)	Men (X2)	X1^2	X2^2
1	154	108	23716	11664
2	109	140	11881	19600
3	137	114	18769	12996
4	115	91	13225	8281
5	152	180	23104	32400
6	140	115	19600	13225
7	154	126	23716	15876
8	178	92	31684	8464
9	101	169	10201	28561
10	103	146	10609	21316
11	126	109	15876	11881
12	126	132	15876	17424
13	137	75	18769	5625
14	165	88	27225	7744
15	165	113	27225	12769
16	129	151	16641	22801
17	200	70	40000	4900
18	148	115	21904	13225
19		187		34969
20		104		10816
Total	2539	2425	370021	314537
Mean	141.05556	121.25
SD	26.4363	32.852

Mean =

SD =

	Women (1)	Men (2)
n	18	20
Mean	141.0556	121.25
SD	26.436	32.852
Var	698.8791	1079.2500

Test

Test Stat

Pooled variance =

= 899.6304

Test Stat =

=2.0324

p-value = P ( > T.S. )

= P( > 2.03) ........using t-dist tables

p- value = 0.0248

Since p-value > level of significance (0.01)

We do not reject the null hypothesis at 1% level. There is insufficient evidence to conclude that the  mean SSHA score for men is lower than the mean score in a comparable group of women.

p- value is in red means outside the blue region which is critical. So we accept the null hypothesis.