The assignment will be based on sampling variability, margins of error, and otherimportant topics in sampling. The topics are covered in Chapter 3 of the book Statistics: Concepts and Controversies by Moore & Notz.Question 1In December 2016, Gallup conducted a survey of US adults, and asked themtheir frequency of dining out at a restaurant in the past week. Copy the following URLinto your browser, and take a quick look at the results:https://news.gallup.com/poll/201710/americans-dining-frequency-little-changed-2008.aspx. In particular, read through the “Survey Methods” section at the bottom ofthe article.a. What was the population of interest for this survey? What was the size of thesample?b. Based on the first table in the article, what percentage of US adults in thesample stated that they ate dinner in a restaurant at least twice in the pastweek, in the December 2016 survey? Show all your work.c. For a moment, let’s ignore whether or not this was an SRS. If it was an SRS,what would be the approximate margin of error at the 95% confidence level?Show all your work.d. Was this a simple random sample (SRS)? Explain why or why not, in terms ofhow the sample was obtained. (A detailed description of the samplingmethodology can be found in the “Survey Methods” section at the bottom.)Question 2Suppose you are a memberof your university’s student organization, and you want to survey students on whetherthey would like to hold a concert at the end of the year. You decide to survey studentsusing a simple random sample from the student roster, to ensure that there is nosampling bias. You are interested in a 95% confidence level for your estimates.a. A friend of yours, Alex, suggests that you survey 50 of the university’s 50,000students. Another friend, Jesse, suggests that you instead survey 100 of theuniversity’s 50,000 students. Jesse says that this is worth the effort, since it willcut your margin of error in half. Is this correct? Explain why or why not.Remember to show all your work.b. How many students would you have to survey to have a margin of error that ishalf of what it would be for a sample of size 50? Show all your work.MathStatistics and Probability STAT 100
