Question

In a recent telephone survey, 5,000 randomly selected teenagers were asked to cite their primary social network sites. Six of 10 teenagers said they use Mybook as their primary social network site. A 95% confidence interval to estimate the true proportion of teenagers who use Mybook as their primary social network site is found to be (0.2964, 0.9036). Which of the following is a correct interpretation of the confidence level?

a. Ninety-five percent of all samples of this size would yield a confidence interval of (0.2964, 0.9036).
b. There is a 95% chance that the true proportion of teenagers who use Mybook as their primary social network site is in the interval (0.2964, 0.9036).
c. Ninety-five percent of the time, the procedure used to generate this interval will capture the true proportion of teenagers who use Mybook as their primary social network site.
d. Ninety-five percent of all the samples of size 5,000 lies in the confidence interval (0.2964, 0.9036).
e. There is a 95% chance that randomly selected teenagers will be part of the 60% who use Mybook as their primary social network site.

Answer 1

Ninety-five percent of the time, the procedure used to generate this interval will capture the true proportion of teenagers who use Mybook as their primary social network site.

Explanation:

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Answer 2

b. There is a 95% chance that the true proportion of teenagers who use Mybook as their primary social network site is in the interval (0.2964, 0.9036).

Explanation:

Hello!

In general, a 95% confidence interval for the population proportion can be interpreted as: There is a 95% chance (or confidence) that the interval will contain the true value of the proportion.

(Remember the confidence level of 95% means that if you were to make 100 intervals for the population proportion, 95 of them will contain its true value)

The estimated parameter is the population proportion of teenagers that use Mybook as their primary social network site.

With this in mind then you can say that there is a 95% probability that the interval (0.2964, 0.9036) will contain the true value of the proportion of teenagers that use Mybook as their primary social network site.

The correct answer is: b

I hope this helps!