Question

In a recent school newspaper survey, 3,000 randomly selected teenagers were asked to cite their primary transportation method to school. Fifteen of 20 teenagers said they use their own car to get to school. A 90% confidence interval to estimate the true proportion of teenagers who drive their own car to school is found to be (0.5907, 0.9093). Which of the following is a correct interpretation of the confidence level?
Ninety percent of the time, the procedure used to generate this interval will capture the true proportion of teenagers who drive their own car to school.

Ninety percent of all samples of this size would yield a confidence interval of (0.5907, 0.9093). (not correct)

There is a 90% chance that the true proportion of teenagers who drive their own car to school will be (0.5907, 0.9093).

Ninety percent of all the samples of size 3,000 lie in the confidence interval (0.5907, 0.9093).

There is a 90% chance that randomly selected teenagers will be part of the 75% who drive their own car to school.

Answer 1

Answer: There is a 90% chance that the true proportion of teenagers who drive their own car to school will lie in (0.5907, 0.9093).

Step-by-step explanation:

Interpretation of a% confidence interval : A person can be a% confident that the true population parameter lies in it.

Here, A 90% confidence interval to estimate the true proportion of teenagers who drive their own car to school is found to be (0.5907, 0.9093).

i.e. A person can be 90% confident that  the true proportion of teenagers who drive their own car to school lies in (0.5907, 0.9093).

Hence, correct interpretation is : There is a 90% chance that the true proportion of teenagers who drive their own car to school will lie in (0.5907, 0.9093).