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Vacation times at major companies. The primary determinant
Chapter 6, Problem 129SE(choose chapter or problem)
Vacation times at major companies. The primary determinant of the amount of vacation time U.S. employees receive is their length of service. According to data released by Hewitt Associates, more than 8 of 10 employers provide 2 weeks of vacation after the first year. After 5 years, 75% of employers provide 3 weeks, and after 15 years most provide 4-week vacations. To more accurately estimate p, the proportion of U.S. employers who provide only 2 weeks of vacation to new hires, a random sample of 24 major U.S. companies was contacted. The following vacation times were reported (in days).
a. Construct a 95% confidence interval for p.
b. Is the sample size large enough to ensure that the normal distribution provides a reasonable approximation to the sampling distribution of \(\hat{p}\)? Justify your answer.
c. How large a sample would be required to estimate p to within .02 with 95% confidence?
Questions & Answers
QUESTION:
Vacation times at major companies. The primary determinant of the amount of vacation time U.S. employees receive is their length of service. According to data released by Hewitt Associates, more than 8 of 10 employers provide 2 weeks of vacation after the first year. After 5 years, 75% of employers provide 3 weeks, and after 15 years most provide 4-week vacations. To more accurately estimate p, the proportion of U.S. employers who provide only 2 weeks of vacation to new hires, a random sample of 24 major U.S. companies was contacted. The following vacation times were reported (in days).
a. Construct a 95% confidence interval for p.
b. Is the sample size large enough to ensure that the normal distribution provides a reasonable approximation to the sampling distribution of \(\hat{p}\)? Justify your answer.
c. How large a sample would be required to estimate p to within .02 with 95% confidence?
ANSWER:Solution:
Step 1 of 3:
According to data released by Hewitt Associates, more than 8 of 10 employers provide 2 weeks of vacation. After 5 years, 75% of the employers provide 3 weeks, and after 15 years most provided 4-week vacations.
A random sample of vacation times of 24 U.S Major companies is given.
10 |
12 |
10 |
10 |
10 |
10 |
15 |
10 |
10 |
10 |
10 |
10 |
10 |
10 |
10 |
10 |
10 |
15 |
10 |
10 |
15 |
10 |
10 |
10 |
- We have to construct a 95 % CI for p.
-
We have to check whether the sample size large enough to ensure that the normal distribution provides a reasonable approximation to the sampling distribution of
.
- We have to find the sample size that would be required to estimate p to within .02 with 95% confidence.