2. Does college experience depend on a major? The mean satisfaction with college

Question

2. Does college experience depend on a major? The mean satisfaction with college experience in a random sample of 48 math majors is 8.3 with a standard deviation of 2. The mean satisfaction with college experience of all students in the previous year is 7.8. Are math majors different from all other students in terms of their college satisfaction? Use =0.01.

1) state your hypotheses; 2) draw a graph showing the critical z-scores and the rejection region; 3) calculate z-obtained; 4) make a conclusion. Round all calculations to 2 decimal points.

Explanation / Answer

Here we have to test the hypothesis that,

H0 : mu = 7.8 Vs H1 : mu not= 7.8

where mu is population mean.

Assume alpha = level of significance = 0.01

Given that,

sample size (n) = 48

Sample mean (Xbar) = 8.3

standarde deviation (sigma) = 2

Here sample size is > 30 so we use one sample z-test.

The test statistic follows Z-distribution.

The test statistic is,

Z = (Xbar - mu) / (sigma/sqrt(n))

= (8.3 - 7.8) / (2 / sqrt(48))

= 1.73

Now we have to find critical value.

We can find critical value by using EXCEL.

syntax :

=NORMSINV(probability)

where probability = alpha/2

Critical value = 2.58 and -2.58

Since the test is two sided.

So here test statistic < alpha

Accept H0 at 1% level of significance.

Conclusion ; There is not sufficient evidence to say that the population mean is differ than 7.8

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