Question

3. A Pew poll found that in a sample of 1002 adults, 621 had a social media account. The study was repeated a year later, and 631 out of 971 adults has social media accounts.

(a) Are the samples independent or paired?

(b) Consider constructing a 90% confidence interval for the increase in the proportion of adults with social media accounts during the year between the surveys.

               i. Find the point of estimate using proper notation. Show your work including all relevant quantities needed. Round your answer to 4 decimal places.

               ii. Find the margin of error. Show your work including all relevant quantities needed using proper notation. Round your answer to 4 decimal places.

               iii. Construct the confidence interval by filling in the blanks below. Round your answers to 4 decimal places.

_________________ < _________________ < _________________

               iv. An executive at a social media company claims that the proportion of adults with social media accounts increased during the year. Does the confidence interval contradict this claim? Justify your answer.

(c) Consider the question: can you conclude that the proportion of adults with social media accounts was less the previous year at a significance level of 10%?

               i. State the null and alternate hypothesis using proper notation.

               ii. Circle the type of critical value(s)/test statistic and corresponding region needed to answer the problem.

• z-score or t-score


           • Identify the degrees of freedom, if not applicable write NA:

• right-tailed, left-tailed, or two-tailed

               iii. Find the critical value(s) using proper notation. Round your answers to 3 decimal places.

               iv. Find the test statistic using proper notation. Show your work including all relevant quantities needed. Round your answer to 4 decimal places.

               v. Compute the P-value of the test statistic. Round your answer to 4 decimal places.

               vi. Can you reject the null hypothesis? Justify your answer.

               vii. Answer the question.

Answer 1

1. Let denote the proportion of adults with social media accounts in previous year and in current year respectively.

a) The samples are independent.

i) The point of estimate of the difference in the proportion of adults with social media accounts during the year between the surveys

c)