17. A researcher administered a test measuring knowledge of current events to th

Question

17. A researcher administered a test measuring knowledge of current events to the entire student body. Thinking that their scores would differ from the scores of the student body, she selected a random sample of 40 sociology majors, and compared their scores to those of the entire student body. She found that the mean score for the entire student body was 17.6 (with a standard deviation of 4.1). The mean score for sociology majors was 19.2 (with a standard deviation of 3.5). Do the scores of sociology majors differ from those of the student body? Perform the appropriate hypothesis test, using an alpha of.05. (Explain why you selected that test.)

Explanation / Answer

Solution:

Here, we have to use one sample z test for population mean because sample size is greater than 30 and population standard deviation is given.

The null and alternative hypothesis for this test is given as below:

Null hypothesis: H0: Mean score for sociology majors is 17.6.

Alternative hypothesis: Ha: Mean score for sociology majors is different than 17.6.

H0: µ = 17.6 versus Ha: µ 17.6

This is a two tailed test.

Test statistic = Z = (Xbar - µ) / [/sqrt(n)]

We are given

Xbar = 19.2

= 4.1

n = 40

= 0.05

Z = (19.2 – 17.6) / [4.1/sqrt(40)]

Z = 2.4681

P-value = 0.0136 (by using z-table or excel)

P-value < = 0.05

So, we reject the null hypothesis.

There is sufficient evidence to conclude that Mean score for sociology majors is different than 17.6.

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