Question

A Deputy Chancellor for Student Affairs from a small tertiary institution was concerned about student spending on internet costs during the study period from home since the Covid-19 outbreak. He wanted to find out whether student spending on the Social Sciences group was more than student spending on the Science and Technology family. As a quick and preliminary study, he collected samples of 9 students from the Science and Technology family and 11 students from the Social Sciences family. The following table contains expenses for student internet during April 2020 (in $. 000):

Science & Technology	21	28	20	18	17	23	27	29	20
Social Sciences	22	24	21	19	25	17	20	18	23	22	15

Note: Spending on the internet is purely for learning from home, which is calculated based on an increase from the previous month's expenditure.

Question:
1. Explain whether you can or cannot use the normal distribution approach in the above case?
2. Perform testing by showing formal steps in testing hypotheses (design hypotheses, decision rules (critical values), test statistics, and conclusions) at α = 0.05.

Answer 1

(1)

We cannot use the normal distribution approach in the above case because the population standard deviation is not given and sample size is small < n.

(2)

Step1:

H0: Null Hypothesis: 1 - 2 0 ( Student spending on the Social Sciences group was not more than student spending on the Science and Technology family.)

HA: Alternative Hypothesis: 1 - 2 < 0 ( Student spending on the Social Sciences group was more than student spending on the Science and Technology family.) (Claim)

Step 2:

From the given data, the following statistics are calculated:

n1 = 9

1 = 22.5556

s1 = 4.4472

n2 = 11

2 = 20.5454

s2 = 3.0778

=0.05

df = 9 + 11 - 2

From Table, critical value of t == - 1.734

Decision Rule:
Reject H0:if t < - 1.734

Step 3:

Pooled Standard Deviation is given by:

Test Statistic is given by:

Step 4:

Since calculalted value of t = 1.193 is greatr than critical value of t = - 1.734, the difference is not significant. Fail to reject null hypothesis.

Conclusion:
The data do not support the claim that student spending on the Social Sciences group was more than student spending on the Science and Technology family.