6.  A large software company gives job applicants a test of...

6.  A large software company gives job applicants a test of programming ability, and the mean for that test has been 160 in the past. A random sample of 36 job applicants are selected from a large university, and they produce a sample mean score of 165 with a sample standard deviation of 12. At the 0.05 significance level, test the claim that the mean score for students from this university is greater than 160.

a) State the null and alternative hypotheses symbolically.

b) Which test procedure is appropriate to perform the required hypothesis test?  Please justify answer by verifying all assumptions or requirements.

c) Compute the value of the test statistic.

d) Determine the P-value (round to four decimal places).

e) Make a decision regarding the null hypothesis (reject or fail to reject H₀) and show reason.

f) State final conclusion about the claim.