Question

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=900. Construct a 95% 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. ( ROUND TO 4 DECIMAL )

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=10,000. Construct a 95% 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. ( ROUND TO 4 DECIMAL )

D. Based on the confidence interval created using a sample size of 10,000​, 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?

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

Answer 1

A)

n = 900, X = 0.26*900 = 234

For 95% confidence interval, Z_c = 1.96

So, the confidence interval is [0.2313, 0.2887]

B)

Since 0.25 lies inside the confidence interval, we cannot say that more than a quarter of all social media users have purchased an item promoted by a celebrity on a social media​ site. It can be less as well

Answer is NO

C)

n = 10000

So, the confidence interval is [0.2514, 0.2686]

D)

Since the lower limit is higher than 0.25. we can now say that more than a quarter of all social media users have purchased an item promoted by a celebrity on a social media​ site

Answer is YES

E)

As we increase the sample size, the margin of error reduces and the width of the confidence interval decreases

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