Using R for Introductory Statistics : John Verzani

Confidence intervals 185alternative hypothesis: true p is not equal to 0.595 percent confidence interval:0.4290 0.4913sample estimates:P0.46The output contains more than we needed. We see, though, that just after the line 95percent confidence interval: are two values, 0.4290 and 0.4913, which are the endpointsof our interval. These are slightly different from our previously found endpoints, as theformula used by prop. test() is found by solving Equation 7.1 exactly rather than by usingthe standard error to approximate the answer.The extra argument conf. level=0.95 sets the confidence level. The default is 0.95, soin this case it could have been left off.binom.test()The function binom. test() will also find confidence intervals. In this case, it uses thebinomial distribution in place of the normal approximation.7.2.2 Problems7.1 Find an example in the media in which the results of a poll are presented. Identify thepopulation, the size of the sample, the confidence interval, the margin of error, and theconfidence level.7.2 In Example 7.2 a random sample from the United States population is taken byusing listed residential phone numbers. Which segments of the population would bemissed by this sampling method?7.3 The web site http://www.cnn.com/ conducts daily polls. Explain why the site’sdisclaimer reads:This Quick Vote is not scientific and reflects the opinions of only thoseInternet users who have chosen to participate. The results cannot beassumed to represent the opinions of Internet users in general, nor thepublic as a whole.7.4 Suppose a Zogby poll with 1,013 randomly selected participants and thehttp://www.cnn.com/ poll (see the previous problem) with 80,000 respondents ask thesame question. If there is a discrepancy in the sample proportion, which would youbelieve is closer to the unknown population parameter?7.5 Find 80% and 90% confidence intervals for a survey with n=100 and7.6 A student wishes to find the proportion of left-handed people. She surveys 100fellow students and finds that only 5 are left-handed. Does a 95% confidence intervalcontain the value of p=1/10?7.7 Of the last ten times you’ve dropped your toast, it has landed sticky-side downnine times. If these are a random sample from the Bernoulli(p) distribution, find an 80%confidence interval for p, the probability of the sticky side landing down.