Problem #1:

An application development manager claims that 75% of programs in the
production portfolio are Y2K compliant. The EDP auditor disputes this
claim and believes that the proportion is less than claimed. She
examines 200 of these programs and discovers that 142 are compliant.

1.  	Give the appropriate null and one-sided research hypothesis
	that corresponds to the auditors belief.

		H0: pi = 0.75
		Ha: pi < 0.75

2.	Calculate the p-value for the hypotheses stated above.

	Note that in this case you have a large sample. Since the sample
	proportion is 142/200=0.71, then p<0.75 and so is consistent with 
         Ha. Assuming H0 true, sigma(p)=sqrt((0.75)*(0.25)/200)=0.031
	and mu(p)=pi=0.75, so z is:

	       z = (0.71-0.75)/S(p)
		 = -1.3

	Hence the p-value is 50-(80.64)/2=9.68%. 


3.	Is this significant, highly significant, or non-significant?

		Non-significant.


4.	Comment on the analyst's belief.

	Since this is a non-significant result, the EDP auditor has
	insufficient evidence to reject H0 and so has insufficient
     	evidence to challenge the managers claim.


Problem #2:

A production manager claims that 50% of disk drives coming off a production
line have faster seek times than stipulated in the specifications. The QA
manager believes that the actual proportion is less than claimed. She takes
a sample of 350 drives from a recent production run and finds that 102 are
faster.
 
1.  	Give the appropriate null and one-sided research hypothesis
	that corresponds to the QA managers belief.

		H0: pi = 0.5
		Ha: pi < 0.5

2.	Conduct a test of hypotheses.

	Since p=102/350=0.29, then p<0.5 and so is consistent with Ha.
         Also, assuming H0 true, sigma(p)=sqrt((0.5)*(0.5)/350)=0.027 and
         mu(p)=pi=0.5 so:

		z=(0.29-0.5)/0.027=-7.8

	The p-value is essentially zero. This is a highly significant result 
	and the null hypothesis should be rejected. The QA manager therefore
	has enough evidence to support her belief that the true proportion
	is less than claimed.