Question

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.

Answer 1

Answer:

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%.