Download Exam 3A Fall 2002

Stat 100
Exam 3 A
Fall 2002
1. A sample of 90 measurements was taken in order to test a claim that the population
mean is less than 420. The sample mean and standard deviation were found to be 360 and
210, respectively. An hypothesis test will be performed at the 1% level of significance.
a) (6 pts) Formulate the hypotheses.
b) (6 pts) Define the appropriate test statistic and determine its observed value.
c) (4 pts) Determine the rejection region.
d) (6 pts) State the conclusion and calculate the P-value.
2. A cable company wanted to estimate the proportion of its cable subscribers that have
complaints against the cable company this year. They conducted a large survey and
determined that the 97% confidence interval for the true proportion of such subscribers is
(.0349, .1651). Using this information, find:
a) (5 pts) a point estimate of the population proportion p and the 97% error margin
b) (8 pts) the sample size n that was used in the study.
c) (8 pts) Determine the sample size to be 99% confident that the error of estimation is
within .05 if the company has no idea about the true population proportion.
3. (15 pts) Weights from a sample of 11 female wolves are recorded and the mean and
standard deviation are found to be 91.91 lb and 12.38 lb, respectively.
Determine a 98% confidence interval for the population mean weight of female wolves.
4. The mean height of 75 male students who showed above-average participation in
college athletics was 69.1 inches with a standard deviation of 2.5 inches, while 65 male
students who showed no interest in such participation had a mean height of 68.4 inches
with a standard deviation of 2.8 inches. Test the hypothesis that male students who
participate in college athletics are taller than the other male students at a 0.05 level of
significance.
a) (6 pts) Formulate the null and alternative hypotheses.
b) (4 pts) Determine the rejection region.
c) (6 pts) Determine the observed value of the test statistic.
d) (6 pts) State your conclusion and report the P-value.
5. A study to determine the effect of listening to a Mozart piano sonata prior to taking an
exam had the following results.
Mean
Standard deviation
Sample size
Mozart
83.12
5.7
25
No Mozart
79.9
6.2
28
a) (15 pts) Construct a 95% confidence interval for the difference in mean exam scores.
b) (5 pts) If you were to test the null hypothesis that the mean exam scores are equal
versus the alternative hypothesis of not equal, what would the conclusion be with
  .05 ? Explain.