Question

A school district has a standardized test that it uses to sort students into magnet schools, where the test is on a 200-point scale. The superintendent is looking to determine whether male and female students have approximately equal scores on the test. The scores for a random sample of 20 male students and 20 female students are recorded. Assume that the population variances of scores for male and female students are equal and that the scores are normally distributed for both male and female students. Let the male students be the first sample, and let the female students be the second sample.

The superintendent conducts a two-mean hypothesis test at the 0.05 level of significance, to test if there is evidence that male and female students have different scores, on average.

For this test: H0:μ1=μ2; Ha:μ1≠μ2, which is a two-tailed test.

Male Score	Female Score
112	116
123	108
124	124
124	127
125	127
101	127
103	107
106	119
127	120
116	121
121	122
122	109
109	115
115	111
111	122
122	101
101	108
108	121
121	100
100	125

The above table contains scores for a random sample of 20 male students and 20 female students.

Use a TI-83, TI-83 Plus, or TI-84 calculator to test if there is evidence that male and female students have different scores, on average. Identify the test statistic, t, and p-value from the calculator output. Round your test statistic to two decimal places and your p-value to three decimal places.

test statistic =? , p-value = ?

Answer 1

Sol:

Install analysis toolpak and then go to

Data>Data analysis>t test Two sample assuming unequal variances

un

You get

t-Test: Two-Sample Assuming Unequal Variances
	Male Score	Female Score
Mean	114.55	116.5
Variance	83.62895	74.47368
Observations	20	20
Hypothesized Mean Difference	0
df	38
t Stat	-0.69355
P(T<=t) one-tail	0.24609
t Critical one-tail	1.685954
P(T<=t) two-tail	0.49218
t Critical two-tail	2.024394

You can also enter into it83 cal as

STAT>TESTS>2-SampTTest

From output

t=-0.69

p=0.492