Stat 2216 | Spring 1996 |

Statistical Methods................................................................ | R Claycombe |

Write all answers in your blue book and show all work there. Return your exam in your blue book.

16 pts.

1) Consider the following sample of distances that goods are shipped from the H company.

distances = {5,6,7,8,9,10,11,12,13,14}

a) Enter the data into a Lotus spread sheet and save it for use in SPSS.

b) Use SPSS to list the data and to generate statistics needed for a confidence interval.

c) Construct a 90 percent confidence interval for .

(Be sure to print out all of your computer listing from SPSS and to remove page breaks before printing.)

16 pts.

2) a) Use the gss.sys file to generate a histogram for races included in that file.

b) Now suppose that you are looking for evidence in that sample that the population proportion of white is greater than .75. Conduct this test at the 5 percent level of significance and be sure to show all steps in the test.

(Be sure to print out all of your computer listing from SPSS and to remove page breaks before printing.)

20 pts.

3) Suppose that we have a small population such that x = {4,5,6} and that we are sampling with replacement (n = 2).

a) List all the possible samples.

b) List all the possible sample means and their probabilities.

c) Which is more dispersed, the sampling distribution or the population? Why?

d) Find the standard error of the mean.

e) If we sample with replacement, n could equal 4, couldn't it? How many possible samples could there be then? What is the probability that the sample mean would equal 6 with the sample size of 4? Find the standard error of the mean, preferably without listing the sampling distribution.

16 pts.

4) Suppose that we know of an estimator that is biased, inefficient and inconsistent in its estimation of .

a) Draw a well-labeled diagram that shows it to be biased.

b) Draw a well-labeled diagram that shows it to be inefficient.

c) Draw a well-labeled diagram that shows it to be inconsistent.

16 pts.

5) a) Suppose that your firm selects every 32nd item off the production line to sample product quality. Is this usually a reasonable way to select a random sample? What do we call such a sampling technique?

b) Suppose now that your firm punches holes into metal parts and it uses a wheel with eight spikes that rolls over the metal parts as suggested by the superb art work below.

Would a sampling method that takes one in thirty-two be a suitable selection method now? Why? Would a cluster sample be a good idea in this situation? Why?

I have neither given nor received unfair aid on this test.

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