42. Show that in Example 4.4.7, page 153, the difference between the twocandidates is statistically significant even at a confidence level of 99.7%. The sample size is n =1350, and the poll presents only two options, sothere is a common standard error.581For Candidate A, we have k = 581, so p2 0.4303 or 43.03%. For1350769Candidate B, we have k = 769, so p2 0.5696 or 56.96%.13500.4304 × (1 – 0.4304)VThe standard error is st.err. 22 0.0135 or13501.35%.The confidence interval for Candidate A goes from 43.03 – 2 × 1.35 to43.03 + 2 x 1.35, that is from 40.33% to 45.73%.The confidence interval for Candidate B goes from 56.96 – 2 × 1.35 to56.96 + 2 x 1.35, that is from 54.26% to 59.66%.As we can see below, the confidence interval for Candidate B is com-pletely to the right of the interval for Candidate A. Candidate B now has astatistically significant advantage over Candidate A.A40.33E*****:******I43.0345.73ВE*******I********I54.2656.9659.66Figure 4.19: Non-overlapping Confidence Intervals for Two CandidatesBoth candidates still have one more week to go before the election. Whoknows what may happen.Another way to see that the difference between the two candidates isstatistically significant is by observing that their levels of support in the polldiffer by more than 4 standard errors. PB -PA~ 57% – 43% = 14% whereas4 x st.err. = 4 × 1.35 = 5.4.

Name: 42. Show that in Example 4.4.7, page 153, the difference between the t
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Description: 42. Show that in Example 4.4.7, page 153, the difference between the twocandidates is statistically significant even at a confidence level of 99.7%. The sample size is n =1350, and the poll presents only two options, sothere is a common standard erro