Assignment 2, Fall 2000

STATISTICS 403 - Assignment 2

Due Thursday, September 14, 2000

Use the sign test to analyze the data in problem 3.7 of the text. Also construct a confidence interval for the median difference. Use a confidence coefficient as close to 98% as possible. Report the actual level of confidence for your interval.
Use the sign test to analyze the data in problem 3.11 of the text. Also construct a confidence interval for the median difference. Use a confidence coefficient as close to 90% as possible. Report the actual level of confidence for your interval.
Salaries of professional athletes receive a good deal of attention in the press. The 1990 salaries of a random sample of 20 non-pitchers in baseball are given below, units are thousands of dollars.
```
100   100   111    114    165    210    225    225    230    250
410   575   750    900   1200   1900   2100   2100   2650   3300
```
We wish to investigate the central value of the distribution of salaries of non-pitchers in baseball.
- (a) Use a t-test to test the hypothesis that the central value salary is equal to $2,000,000 versus the alternative that it is less than $2,000,000. Be sure to include the value of the test statistic, P-value, decision and a conclusion within the context of the problem.
- (b) Construct a 95% confidence interval for the central value salary using a t-interval.
- (c) Why might the procedures in (a) and (b) be inappropriate? Support your answer statistically (i.e. construct and interpret a graphical summary of the data that addresses the assumptions necessary for performing t-procedures).
- (d) Use a sign test to see if the central value is $2,000,000 versus an alternative that the central value is less than $2,000,000. Be sure to include the value of the test statistic, P-value, decision and a conclusion within the context of the problem.
- (e) Estimate the central value and construct a confidence interval with confidence coefficient close to 95%. Report the actual confidence level for your interval.
The sign test for the one-sample location problem can be stated in terms of the binomial test in the following way. For H: = versus A: > we define the probability of a success as = P(X > ) and test H: = 1/2 versus A: > 1/2. Instead suppose we are interested in the upper quartile, qU such that Pr(X < qU) = 0.75 and Pr(X > qU) = 0.25. A random sample of 15 students take an achievement test upon entering college. Their scores are given below. Test the hypothesis H: qU=193 versus A: qU > 193. Be sure to include the value of your test statistic, exact P-value, decision and a conclusion within the context of the problem.
```
189    233    195    160    212
179    231    185    199    213
202    193    174    166    248
```