Assume that a simple random sample has been selected from a normally distributed population and test the given claim. Use either the traditional method or P-value method as indicated. Identify the null and alternative hypotheses, test statistic, critical value(s) or P-value (or range of P-values) as appropriate, and state the final conclusion that addresses the original claim. Choose the correct option based on the problem information.

A large software company gives job applicants a test of programming ability and the mean for that test has been 160 in the past. Twenty-five job applicants are randomly selected from one large university and they produce a mean score and standard deviation of 183 and 12, respectively. Use a 0.05 level of significance to test the claim that this sample comes from a population with a mean score greater than 160. Use the P-value method of testing hypotheses. Choose the correct P-value and conclusion based on the null hypothesis.

A. P-value < 0.005. Fail to reject H0.
B. 0.01 < P-value < 0.025. Reject H0.
C. P-value < 0.005. Reject H0.
D. P-value = 0.05. Reject H0.

To answer this question you must identify the following
Population mean: 160 important for hypothesis testing
Sample size = 25
Sample mean =183
Sample SD = 12

First find the Z score given the following (183-160)/12 or (sample mean -pop mean)/SD

Then using the z score 1.916 on the z score chart we see it corresponds to about 0.9719 which we know holds the values from 0-160. We want to know greater than 160 so we subtract it from 1.

1-0.9719 = 0.0281 which is less then the alpha of 0.05.

So we can reject the null hypothesis because it is significantly significant. Which gives us C