Question

use the sample data and confidence level given below to complete parts (a) through (d).
in a study of cell phone use and brain hemispheric dominance, an internet survey was e - mailed to 2595 subjects randomly selected from an online group involved with ears. 931 surveys were returned. construct a 90% confidence interval for the proportion of returned surveys.
click the icon to view a table of z scores.

d) write a statement that correctly interprets the confidence interval. choose the correct answer below
a. there is a 90% chance that the true value of the population proportion will fall between the lower bound and the upper bound.
b. one has 90% confidence that the sample proportion is equal to the population proportion.
c. 90% of sample proportions will fall between the lower bound and the upper bound.
d. one has 90% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.

Explanation:

• A confidence interval is not about the probability that the population proportion falls within the interval (Option A is wrong).
• The sample proportion is just an estimate, and we don't say it's equal to the population proportion with a certain confidence (Option B is wrong).
• It's not about sample proportions falling within the interval (Option C is wrong).
• The correct interpretation of a confidence interval is that we have a certain level of confidence (in this case 90%) that the interval contains the true population proportion.

Answer:

D. One has 90% confidence that the interval from the lower bound to the upper bound actually does contain the true value of the population proportion.