Using R for Introductory Statistics : John Verzani

Confidence intervals 183In R this becomes one of> zstar = −qnorm(alpha/2) # left tail> zstar = qnorm(1−alpha/2) # right tailThe inverse relationship would be found by> alpha = 2*pnorm(−zstar)Figure 7.3 The relationship betweenz* or z a/2 , and α■ Example 7.2: Presidential job performance A Zogby America poll involved 1,013likely voters selected randomly from throughout the 48 contiguous United States usinglisted residential telephone numbers.The surveyers found that 466 voters rated thepresident’s job performance as “good” or “excellent.” Find a 95% confidence interval forthe true proportion.This type of polling is about as close to a random sample as can be gotten with limitedresources, though there are several sources of possible bias to consider. For example, noteveryone in the United States has a listed residential telephone number, so the sample isonly from households that do. Additionally, nonresponse can be very high in suchsurveys, introducing another potential bias. For simplicity, we’ll assume the sample is arandom sample from the population of likely voters and that n=1013 is large enough sothat the normal approximation applies.As a 95% confidence interval for p would be To find thiswe have> n = 1013> phat = 466/n> SE = sqrt(phat*(1−phat) /n)> alpha = .05> zstar = −qnorm(alpha/2)> zstar # nearly 2 if doing byhand