Question

Let’s say that you want to estimate the proportion of You Tube videos which take place outside (define "outside" to be if any part of the video takes place outdoors). You take a random sample of 128 You Tube videos5 and determine that 37 of them take place outside. You’d like to estimate the proportion of all You Tube videos which take place outside, so you decide to create a bootstrap interval from the original sample of 128 videos.

a. Describe in words the relevant statistic and parameter for this problem. If you know the numerical value for either one, provide it. If you don’t know the numerical value, explain why the value is unknown.

b. What notation is used to describe, respectively, the statistic and the parameter?

c. If using software to bootstrap the original dataset, what is the statistic calculated on each bootstrap sample?

d. When creating a bootstrap sampling distribution (histogram) of the bootstrapped sample proportions, where should the center of the histogram lie?

f. In words of the problem, interpret the confidence interval which was estimated in the previous part.

Answer 1

The relevant statistic for this problem is the proportion of videos in the sample that take place outside. The confidence interval estimated from the bootstrap method allows us to estimate the range of plausible values for the true proportion of all You Tube videos that take place outdoors.

Step-by-step explanation:

The relevant statistic for this problem is the proportion of videos in the sample that take place outside. In this case, 37 out of 128 videos in the sample take place outside. The parameter is the true proportion of all You Tube videos that take place outside, which is unknown.

The notation used to describe the statistic is p-hat, and the notation used to describe the parameter is p.

When creating a bootstrap sampling distribution, the statistic calculated on each bootstrap sample would be the proportion of videos in that sample that take place outside.

The center of the histogram for the bootstrapped sample proportions will likely lie around the sample proportion of videos that take place outside, which is 37/128.

The confidence interval estimated from the bootstrap method provides a range of plausible values for the true proportion of all You Tube videos that take place outdoors. It means that we are 95% confident that the true proportion falls within the calculated interval.