Question

1. A recent poll was conducted by the Gallup organization between April 2nd and April 8th, 2018. A total of 785 Facebook users living in the U.S. were selected using random digit dialing and were interviewed over the phone (either landline or cell phone). Respondents were asked the following question: “How concerned are you about invasion of privacy when using Facebook? Very concerned, somewhat concerned, not too concerned or not concerned.” 43% of those selected said “very concerned”. Suppose we want to study the proportion of all Facebook users who are “very concerned” about the invasion of privacy.

a) Define the parameter of interest in the context of the problem (include the symbol used to denote it).

b) What is the statistic in this problem (include the symbol used to denote it)?

c) Check the assumptions necessary to construct a normal-based confidence interval for the parameter of interest by verifying the appropriate conditions. Actually show that you checked these in the context of the problem.

d) Find the margin of error if we want 95% confidence in our estimate of the parameter of interest.

e) Find the 95% confidence interval for the parameter of interest.

f) In the context of the problem, give a conclusion based on the confidence interval you found in part e. Your sentence should start with the words “We are 95% confident that……”

Answer 1