Question

A professor of philosophy hypothesizes that an introductory course in logic will affect college students with their other studies. To test this hypothesis, a random sample of 25 first year students is selected. These students are required to complete a logic course during their first year. At the time of graduation, the final GPA is computed or each of these students. The mean GPA for this sample is 2.58 with a SS of 6.

Required:
Can the professor conclude that the grades for the sample were significantly different from the rest of the graduating class, which had an average GPA of 2.33?

Answer 1

NO.

Explanation:

The Professor's hypothesis:

An introductory course in Logic will affect college students with their other studies (will affect their Great Point Average - GPA).

25 students are used as the experimental group while the rest of the class are the control group.

The mean GPA in a sample size (SS) of 6 is = 2.58

The mean GPA in the full sample size of 25 would be = 10.75 by crossmultiplying.

This makes me believe the question was written wrongly. I assume SD (standard deviation) of 0.6 instead of SS (sample size) of 6.

Going by this, if standard deviation is 0.6 then the interval within which the GPA of the experimental group (the 25 students) falls is:

[2.58 - 0.6] to [2.58 + 0.6]

= 1.98 to 3.18

The rest of the graduating class (the control group) had a mean GPA of 2.33

Can the professor conclude that the GPA for the sample is significantly different from that of the control group?

The answer is NO because the GPA of the control group falls within the GPA interval of the experimental group!