A University Faculty's HR department is analyzing the age profile of its staff in order to better inform recruitment decisions. If feels an average...

A University Faculty's HR department is analyzing the age profile of its staff in order to better inform recruitment decisions. If feels an average age of 47.5 years for recruits would be appropriate, but is concerned that it has been unable to successfully hire senior staff. Its most recent 32 hires had an average of 42.1 years, with a standard deviation of 8.6 years.

a) Does the sample indicate support for the HR department's concerns? State your hypotheses, test statistic, rejection region or p-value, and conclusion carefully.

b) Calculate a 95% confidence interval for the population mean age at recruitment.

c) The sample data are bimodal. Assuming this feature is also present in the population, comment on whether or not it is a problem for the test and interval above? Why or Why not??