From a random sample of workers at a large corporation you find that 58% of 200 went on a vacation last year away from home for at least a week. An approximate 95% confidence interval is (0.50, 0.66). Which of the following statements is a correct interpretation?

a. 95% of the coworkers fall in the interval (0.50, 0.66).

b. We are 95% confident that the proportion of coworkers who went on a vacation last year away from home for at least a week is between 50% and 66%.

c. We are 95% confident that between 50% and 66% of the samples will have a proportion near 58%.

d. There is a 95% chance that a random selected coworker has gone on a vacation last year away from home for at least a week.

Question

Alayna Pitts

Mathematics

11 November, 23:53

From a random sample of workers at a large corporation you find that 58% of 200 went on a vacation last year away from home for at least a week. An approximate 95% confidence interval is (0.50, 0.66). Which of the following statements is a correct interpretation?

a. 95% of the coworkers fall in the interval (0.50, 0.66).

b. We are 95% confident that the proportion of coworkers who went on a vacation last year away from home for at least a week is between 50% and 66%.

c. We are 95% confident that between 50% and 66% of the samples will have a proportion near 58%.

d. There is a 95% chance that a random selected coworker has gone on a vacation last year away from home for at least a week.

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Answers (1)

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Cooper Espinoza · Answer 1

b. We are 95% confident that the proportion of coworkers who went on a vacation last year away from home for at least a week is between 50% and 66%.

Step-by-step explanation:

A confidence interval at the level of x% for a proportion being between a and b means that we are x% sure that the true proportion of the population is between a and b.

In this problem, we have that:

95% C. I is (0.5, 0.66)

Interpretation: 95% confident that the true proportion is between 0.5 and 0.66.

The correct answer is:

b. We are 95% confident that the proportion of coworkers who went on a vacation last year away from home for at least a week is between 50% and 66%.