The design specifications for a new line of disk drives indicates 
that the mean seek time is 12.5 ms. A quality assurance analyst 
believes that the disk drives are faster.

1.  	Give the appropriate null and one-sided research hypothesis
	that corresponds to this quality assurance analysts belief.


		H0: mu = 12.5ms
		Ha: mu < 12.5ms


2.  	The analyst collects a random sample of 100 disk drives from
	a production run and determines that the mean seek time is
	12.2 ms with a standard deviation of 0.3 ms.

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


		Note that in this case we have a large sample.
		We first need to compute the z value for a mean
		seek time of 12.2 ms.

			       z = (12.2-12.5)/s(ybar)

			 s(ybar) = 0.3/sqrt(100)
			         = 0.3/10
				= 0.03

		Hence:
				  z = (12.2-12.5)/0.03
				    = -0.3/0.03
			    	    = -10	

		We need to find the area under the standard normal
		curve for z less than -10. Notice that this z value
		is larger than any value in the z table. Hence, the 
		required area is approximately zero.

		Hence the p-value is approximately zero (i.e. much
		less than 0.01).



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

			Highly significant.


	c.	Comment on the analyst's belief.


		Since this is a highly significant result, reject H0. 
		The analyst therefore has strong evidence to support
		her point of view.



3.  	Suppose that the sample size is 10 instead of 100, with
	the same mean and standard deviation.

	a.	Re-compute the p-value.

		Since the sample is small we need to re-compute
		s(ybar). Also, we must assume y normally distributed.

			s(ybar) = 0.3/sqrt(9)
				 = 0.3/3
				 = 0.1

		We need to compute the t value:

			  t = (12.2-12.5)/0.1
			    = -0.3/0.1
			    = -3

		We need to find the area under the student t
		curve for t less than -3. From the t table, 
		since we have 9 degrees of freedom, this is 
		between 1% and 0.5%.

		Hence the p-value is between 1% and 0.5% or
                (as a probability) between 0.01 and 0.005.



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


			Highly significant