1. A sample of 82 Oscar winning actresses had a mean age of 35.9 years and standard deviation
11.1 years when winning Oscars. Use a 0.05 significance level to test the claim that the mean age of actresses when they win Oscars is less than 38 years.
a. State the hypotheses and identify the claim. (3pts)
b. Find the test statistic and p-value. (4pts)
c. State your conclusion. (2pt)
d. Find a confidence interval comparable to the hypothesis test for the mean age of actresses when they win Oscars. (5pts)
2. Listed below are the numbers of words (in thousands) males and females in ten randomly selected couples spoke in a day. Use a 0.05 significance level to test the claim that among couples, there is no difference in the number words males and females speak.
|
Males |
12 |
21 |
16 |
19 |
16 |
9 |
19 |
20 |
8 |
16 |
|
Females |
15 |
17 |
25 |
27 |
21 |
14 |
33 |
18 |
17 |
20 |
a. Are the samples above independent or dependent? Explain why. (2pts)
b. State the hypotheses. (2pts)
c. Find the test statistic and p-value. (4pts)
d. State your conclusion. (2pt)
e. Briefly explain your conclusion so someone outside of a statistics class can understand. (2pts)
3. In a random sample of 360 women, 65% favored stricter gun control laws. In a random sample of 220 men, 60% favored stricter gun control laws.
a. Construct a 95% confidence interval for the difference in proportion of women who favor stricter gun control laws versus men who favor stricter gun control laws. (6pts)
b. Does the interval contain zero? What does this mean? (4pts)
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