Solutions to Final Exam, Fall 2000

1.a H0: p=.5 H1: p> .5

Computed value of test statistic: z=2.8

Reject H0 using significance level 0.005

b. n=16587

2. [(14 4)*(6 1) + (14 5)*(6 0)]/(20 5), where notation (n x) means combinations of size x from a set of size n

3. a Probability of profit=0.7

b. Expected profit=87.5

4. a. 0.2865

b. (20 19) (0.2865)^19 (1-0.2865) + 0.2865^20

c. 0.0228

5. .02*.10/(.02*.10+.01*.20+.0025*.7)

6. a. sample mean=68.75; sample median=70

b. H0: mu=66 Ha: mu>66; computed value of test statistic t=2.07;Reject H0

c. Prob. Type II error=.50

7. a. p-value is approximately .04 (not assuming the variances are the same)

b. Heart rate measurements are normally distributed; Populations of men and women are independent; Depending on the test statistic used in (a), you may or may not need to assume the standard deviations of heart rate measurements for men and women are equal

c. lower bound: 13.03