What is Your Sleep Position? In a study conducted in the United Kingdom about sleeping positions, 1000 adults in the UK were asked their starting position when they fall asleep at night. The most common answer was the fetal position (on the side, with legs pulled up), with 41 % of the participants saying they start in this position. Use a normal distribution to find a 95% confidence interval for the proportion of all UK adults who start sleep in this position. Use the fact that the standard error of the estimate is 0.016. Round your answers to three decimal places. The 95% confidence interval is to. u\"... ".1... ...u......... . . u... ....._. "nu\"... "u...\" u... .u' Asurvev conducted in July 2015 asked a random sample ofAmerican adults whether they had ever used online dating {either an online dating site or a dating app on their cell phone}. Coliege-Educo ted or Not? The survey also asked participants for their level of education, and we wish to estimate the difference in the proportion to use online dating between those with a college degree and those with a high school degree or less. The results are shown in the twoway table below. College SHclizlol Total Yes 157 70 227 N0 666 565 1231 Total 823 635 1453 Table 1: Have you ever used on online dating site or a dating app? (all What proportion of college graduates answered yes when asked if they had ever used online dating? What proportion of those with a high school degree or less said yes? What is the sample difference in proportions? Let pc and p\" be the proportion of college graduates using online dating and the proportion of high school graduates using online dating, respectively. Round your answers to three decimal places. (b) Use the fact that the standard error for the estimate is 0.019 to find a 95% confidence interval for the population difference in proportions. Round your answers to three decimal places. The 95% confidence interval is to i eTextbook and Media Hint (c) Is it plausible that there is no difference between college graduates and high school graduates in how likely they are to use online dating? Use the confidence interval from part (b) to answer. O Yes O NoHow Many Household Cats Hunt Birds? "Domestic cats kill many more wild birds in the United States than scientists thought," states a recent article. Researchers used a sample of n = 140 households in the US with cats to estimate that 35 % of household cats in the US hunt outdoors. 1Milius, S., "Cats kill more than one billion birds each year," Science News, 183(4), February 23, 2013, revised March 8, 2014. Data approximated from information give in the article. (a) Find a 90 % confidence interval for the proportion of household cats in the US that hunt outdoors. Round your answers to three decimal places. The 90 % confidence interval is eTextbook and Media Hint (b) Is it plausible that the proportion of household cats in the US hunting outdoors is 0.45? Is it plausible that the proportion of household cats in the US hunting outdoors is 0.30?Standard Error from a Formula and a Bootstrap Distribution Use Statkey or other technology to generate a bootstrap distribution of sample proportions and find the standard error for that distribution. Compare the result to the standard error given by the Central Limit Theorem, using the sample proportion as an estimate of the population proportion p. Proportion of home team wins in soccer, with n = 129 and p = 0.509. Click here to access StatKey. Round your answer for the bootstrap S'E to two decimal places, and your answer for the formula S'E to three decimal places. Bootstrap SE = i Formula SE = iIt is generally recommended that adults sleep at least 8 hours each night. One of the authors recently asked some of her students (undergraduate and graduate students at Harvard) how many hours each had slept the previous night. curious as to whether her students are getting enough sleep. The data are displayed in Figure 1. The 12 students sampled averaged 6.2 hours of sleep with a standard deviation of 1.70 hours. Assuming this sample is representative of all her students, and assuming students need at least 8 hours of sleep a night, does this provide evidence that. on average, her students are not getting enough sleep? Hours of Sleep Figu re 1 Hours ofsleep for Harvard statistics students State the null and alternative hypotheses. ::# mimmmmmmmww 72W up Give the test statistic and the pvalue and state the conclusion ofthe test. Round your answerforthe test statistic to two decimal places and your answer For the pvalue to three decimal places. teststatistic = n pvalue = Conclusion: v Hg. eTextbook and Media Hint Does the sample provide evidence that, on average, her students are not getting enough sleep? O Yes O No eTextbook and Media Hint (a) A 78% confidence interval for a proportion. Round your answer to two decimal places. i eTextbook and Media Hint (b) An 84% confidence interval for a slope. Round your answer to two decimal places. +2* = i eTextbook and Media Hint (c) A 92 % confidence interval for a standard deviation. Round your answer to two decimal places. +2* = + i eTextbook and Media Hint