Laura W. answered • 04/01/13
I can help you with math and science!
Hi Mildred,
It sounds like what you are doing in this question is a two-tailed hypothesis test. Also, from what you've given, it seems like you don't have the standard deviation for the whole university (population SD). Therefore, you would normally want a two-tailed t-test, however, since the sample size is so large, you can probably assume a normal distribution and use a Z-test.
First, you want to come up with your null and alternative hypotheses: H0: μ = 3.1 (true mean is 3.1, so sample and population are not different); HA: μ ≠ 3.1 (true mean is not 3.1, so sample and population are different)
To calculate the Z-statistic, use: Z = (X - μ)/(σ/√n)
Where μ = population mean (whole university), X = sample mean, σ = SD and n = number in sample. You have the formula right in your question.
Now, since you are using a 92% CI, but really you have a two-tailed situation, each tail will have 4%. You want to find that 4% on a Z chart (added to 92%). I found that ~.96 occurs at Z ≤ 1.75. So, if you want to reject H0, your Z value must be smaller than -1.75 or larger than 1.75. Remember, H0 is that your sample mean and population mean are the same (i.e. NOT significantly different).
