The registrars office contends that college freshmen spend 7.5 hours a week
going to parties. You believe that the registrars office is wrong and that
the time spent is less than they claim. A simple random sample of 100 DePaul 
students indicates that on average DePaul freshmen spend 6.6 hours going to 
parties with a SD of 3 hours.

1. a)	State the null and alternative hypotheses to determine if the
	sample average is significantly different from the registrars
	claim and conduct the test.

		Ho: mu=7.5 hours     <-------- null hypothesis
		Ha: mu<7.5 hours     <-------- alternative hypothesis

		STEP 1: Compute the standard deviation.

			SD = 3/sqrt(100) = 0.3

		STEP 2: Compute the test statistic.

			z = (6.6 - 7.5)/0.3 = -0.9/0.3 = -3

		STEP 3: Find the probability that z <= -3 and test Ho.

			The required % area from the z table is:
                                  (100-99.73)/2=0.135
			The probability is therefore 0.00135
			and since this is less than 0.01 we have a 
			highly significant result and must reject Ho.
			We can therefore conclude that the registrar
			is mistaken and the mean party time is very
			likely to be less than 7.5 hours.

		

   b)	Repeat the test for a sample of 26 students.

		STEP 1: Compute the standard deviation.

			SD = 3/sqrt(26-1) = 0.6

		STEP 2: Compute the test statistic.

			t = (6.6 - 7.5)/0.6 = -0.9/0.6 = -1.5

		STEP 3: Find the probability that t <= -1.5 and test Ho.

			The required % from the t-table is between 5% 
			and 10%. (use the t table for row with df=25)
			The probability is therefore greater than 0.05
			and since this is a non-significant result we 
			have insufficient evidence to reject Ho and
			conclude that we have insufficient evidence
			to question the registrars claim.