Question

11. Are you likely to purchase an item promoted by a celebrity on a social media​ site? According to a​ survey, 26​% of social media users have made such a purchase.

a. Suppose that the survey had a sample size of n=800. Construct a 90% confidence interval estimate for the population proportion of social media users that have purchased an item promoted by a celebrity on a social media site.

b. Based on​ (a), can you claim that more than a quarter of all social media users have purchased an item promoted by a celebrity on a social media​ site?

c. Repeat parts​ (a) and​ (b), assuming that the survey had a sample size of n=900.

Construct a 90% confidence interval estimate for the population proportion of social media users that have purchased an item promoted by a celebrity on a social media site.

Based on the confidence interval created using a sample size of 900​, can you claim that more than a quarter of all social media users have purchased an item promoted by a celebrity on a social media​ site?

d. Repeat parts​ (a) and​ (b), assuming that the survey had a sample size of n= 10,000.

e. Discuss the effect of sample size on confidence interval estimation.

Answer 1

(a)

n = 800

= 0.26

= 0.10

Confidence Interval:

So,

Answer is:

(0.234, 0.286)

(b)

Since not all values in the Confidence Interval: (0.234, 0.286) are greater than 0.25, we cannot conclude that more than a quarter of all social media users have purchased an item promoted by a celebrity on a social media​ site

(c)

(i)

n = 900

= 0.26

= 0.10

Confidence Interval:

So,

Answer is:

(0.236, 0.284)

(ii)

Since not all values in the Confidence Interval: (0.236, 0.284) are greater than 0.25, we cannot conclude that more than a quarter of all social media users have purchased an item promoted by a celebrity on a social media​ site

(c)

(i)

n = 10000

= 0.26

= 0.10

Confidence Interval:

So,

Answer is:

(0.253, 0.267)

(ii)

Since all values in the Confidence Interval: (0.253, 0.267) are greater than 0.25, we conclude that more than a quarter of all social media users have purchased an item promoted by a celebrity on a social media​ site

(e)

Increasing the sample size decreases the width of the confidence interval. Increasing the sample size makes the estimation more precise.