stats7final2answers - Stats 7 winter 2015(Baldi Final...

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Page 1 of 5 Stats 7 winter 2015 (Baldi) – Final Solutions Problem 1 A 2015 Pew Research Center survey of social media use in the United States found that 510 of a random sample of 1134 American adult Facebook users said they are “Facebook- friends” with their parents. a) Obtain a 95% confidence interval for the proportion of all American adult Facebook users who are “Facebook-friends” with their parents. Show what you typed in your calculator. 1-PropZInt: (0.4208,0.4787) or 42.1% to 47.9% b) Surveys like this one often have really low response rates. Does the margin of error for this interval include variability arising from a low response rate? Yes / No. Problem 2 Do ethanol gas (E85l) and regular gasoline (90 octane) differ significantly in the car gas mileage they provide? A study selected a random sample of 9 different car models. Two cars of each model were used and, at random, one was fitted with an ethanol system and the other car was fitted with a regular gasoline system. For consistency, all cars were driven over the same course by a professional driver and gas mileage (in miles per gallon) was recorded. Here are the findings. Car model 1 2 3 4 5 6 7 8 9 Gas 90 octane 28.2 29 27.2 30.0 28.0 27.0 31.2 32.2 29.0 Ethanol E85 29.1 29.4 27.3 30.9 29.3 28.1 32.3 32.5 30.3 a) Write the null and alternative hypotheses for the appropriate test, using proper math symbols. H 0 : μ diff. gas-ethanol = 0 H a : μ diff.placf -caff 0 (matched pairs) b) Give the values of the test statistic and test P -value. Show what you typed in your calculator. TTest on the list of 9 pairwise differences, two-sided alternative t = 5.52 (or t = –5.52), P -value = 0.0006 c) At a significance level of 0.05, we A) reject H 0 B) fail to reject H 0 C) reject H a D) fail to reject H a Problem 3 The California redwood (Sequoia sempervirens) is one of the tallest tree species in the word. Park rangers selected a random sample of 122 full-grown California redwoods and measured their heights. The sample mean and standard deviation were 267 feet and 24 feet, respectively. a) Obtain a 95% confidence interval for the mean height of full-grown California redwoods. Show what you typed in your calculator. TInterval from summary statistics: (262.7, 271.3) b) The numerical value of the margin of error for this interval is 4.3 ft. Problem 4 A study compared rates of myopia among randomly selected young children (6 and 7 years old) of Chinese origin living in either Australia or Singapore. The researchers found that 4 of the 124 children in the Australian sample had myopia, compared with 183 among the 628 children from Singapore. This study resource was shared via CourseHero.com
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Page 2 of 5 a) Is myopia among young children of Chinese origin independent of country of residence? Give the values of the statistic and P -value for the appropriate hypothesis test. Show what you typed in your calculator.
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