You want to determine the percentage of seniors who drive to campus. You take a random sample of 125 seniors and ask them if they drive to campus. Your 95% confidence interval turns out to be from 0.69 to 0.85. Select each correct interpretation of this situation. There might be no, one, or more than one correct statement. Explain, the reason if it is not a correct interpretation.

The statements that are true are: A, B, F, G, and H.

Step-by-step explanation:

The statements are:

A. A 90% confidence interval would be narrower than the interval given.

TRUE.

The less confidence, the less conservative is the interval and the narrower it can be. So this statement is true.

B. You are 95% confident that the proportion of all seniors who drive to campus is in the interval from .69 to .85.

TRUE.

That is the definition of confidence interval.

C. 95% of all seniors drive to campus from 69% to 85% of the time, and the rest drive more frequently or less frequently.

FALSE.

The confidence interval only has meaning referred to the population proportion, not the individual values. So we can not claim this is true.

D. All seniors drive to campus an average of 77% of the time.

FALSE.

The average is expected to be, with 95% confidence, between 0.69 and 0.85. The sample proportion is 0.77*, and this outcome is used to calculate the confidence interval, but we don't know if the true average is 0.77.

*Sample proportion:

E. You are 95% confident that the proportion of seniors in the sample who drive to campus is between .69 and .85.

FALSE.

The sample proportion is known and it is 0.77.

F. 77% of the seniors in your sample drive to campus.

TRUE.

This is the sample proportion.

G. If the sampling were repeated many times, you would expect 95% of the resulting samples to have a sample proportion that falls in the interval from .69 to .85.

TRUE.

This is a property of the confidence intervals.

H. If the sampling were repeated many times, you would expect 95% of the resulting confidence intervals to contain the proportion of all seniors who drive to campus.

TRUE.

This is a property of the confidence intervals.