328 CHAPTER 7 Estimating Parameters and Determining Sample Sizes a. Assume that pn and qn are unknown. b. Assume that 22% of adults can wiggle their ears (based on data from Soul Publishing). 32. Touch Your Nose With Your Tongue Find the sample size needed to estimate the percentage of adults who can touch their nose with their tongue. Use a margin of error of 2 percentage points and use a confidence level of 90%. a. Assume that pn and qn are unknown. b. Assume that a previous study showed that 10% of adults can touch their nose with their tongue (based on data from Onedio). c. Does the use of the results from the previous study have much of an effect on the sample size? 33. E-Cigarettes A New York Times article reported that a survey conducted in 2014 included 36,000 adults, with 3.7% of them being regular users of e-cigarettes. Because e-cigarette use is relatively new, there is a need to obtain today’s usage rate. How many adults must be surveyed now if we want a confidence level of 95% and a margin of error of 1.5 percentage points? a. Assume that nothing is known about the rate of e-cigarette usage among adults. b. Use the results from the 2014 survey. c. Does the use of the result from the 2014 survey have much of an effect on the sample size? 34. Astrology A sociologist plans to conduct a survey to estimate the percentage of adults who believe in astrology. How many people must be surveyed if we want a confidence level of 99% and a margin of error of four percentage points? a. Assume that nothing is known about the percentage to be estimated. b. Use the information from a previous Harris survey in which 26% of respondents said that they believed in astrology. 35. Airline Seating You are the operations manager for American Airlines and you are considering a higher fare level for passengers in aisle seats. You want to estimate the percentage of passengers who now prefer aisle seats. How many randomly selected air passengers must you survey? Assume that you want to be 95% confident that the sample percentage is within 2.5 percentage points of the true population percentage. a. Assume that nothing is known about the percentage of passengers who prefer aisle seats. b. Assume that a prior survey suggests that about 38% of air passengers prefer an aisle seat (based on a 3M Privacy Filters survey). 36. Online Gambling Some states now allow online gambling. As a marketing manager for a casino, you need to determine the percentage of adults in those states who gamble online. How many adults must you survey in order to be 99% confident that your estimate is in error by no more than two percentage points? a. Assume that nothing is known about the percentage of adults who gamble online. b. Assume that 18% of all adults gamble online (based on 2017 data from a Gambling Commission study in Great Britain). 37. Smart Phone Apple is planning for the launch of a new and improved iPhone. The marketing team wants to know the worldwide percentage of consumers who intend to purchase the new model, so a survey is being planned. How many people must be surveyed in order to be 90% confident that the estimated percentage is within three percentage points of the true population percentage? a. Assume that nothing is known about the worldwide percentage of consumers who intend to buy the new model. b. Assume that 11% of consumers have a smartphone and plan to upgrade to a new model. c. Given that the required sample size is relatively small, could you simply survey the people that you know?
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