Question

The superintendent of a large school district speculated that high school students involved in extracurricular activities had a lower mean number of absences per year than high school students not in extracurricular activities. She generated a random sample of students from each group and recorded the number of absences each student had in the most recent school year. The data are listed below. Test the superintendent’s claim at the α=.01 significance level. [To receive full credit, your response should be sure to state your hypotheses, check the relevant requirement(s), find a test value, find a critical value or p-value (either is OK), make your decision, and state your conclusion.]

Students in EC Activities: 4 1 2 0 5 6 2 1 0 3 0 1 1 4 8 6 9 2 0 4 2 10 5 6 1

Students not in EC Activities: 5 7 0 9 4 3 12 8 4 2 0 5 5 4 9 14 6 10 9 6 3

Answer 1

This is a sum of test of equality of means for two independent samples where the sample size for the first group is 25 and the second group is 21. The variance of the groups are unknown so we are using t test for unequal variance.

where is the mean number of absences of the students involved in EC activities and is the mean number of absences of the students not involved in EC activities.

This is a left tailed test

t-Test: Two-Sample Assuming Unequal Variances
	Variable 1	Variable 2
Mean	3.32	5.952380952
Variance	8.56	13.44761905
Observations	25	21
Hypothesized Mean Difference	0
df	38
t Stat	-2.655365953
P(T<=t) one-tail	0.005755783
t Critical one-tail	1.68595446
P(T<=t) two-tail	0.011511566
t Critical two-tail	2.024394164

where variable 1 denotes absences the students involved in EC activities and variable 2 denotes absences of students not involved in EC activities.

t test value is=-2.655365953

We are conducting the test at 1% level of significance. The calculated p value is 0.005755783 (one tailed value is considered as it is left tailed test)

Since the calculated p value 0.005755783 is less than 0.01 so null hypothesis is rejected.

So we may conclude what the superintendent had speculated  is probably correct i.e. the high school students who were involved in extracurricular activities had a lower mean number of absences per year than high school students not in extracurricular activities.