In March 2015, the Public Policy Institute of California (PPIC) surveyed 7525 li

Question

In March 2015, the Public Policy Institute of California (PPIC) surveyed 7525 likely voters living in California. PPIC researchers find that 68 out of 200o Central Valley residents approve of the California Legislature and that 156 out of 300 Bay Area residents approve of the California Legislature. PPIC is interested in the difference between the proportion of Central Valley and Bay Area residents who approve of the California Legislature. PPIC researchers calculate that the standard error for the proportion of Central Valley residents who approve of the California Legislature minus Bay Area residents who approve of the California Legislature is about 0.044 Find the 95% confidence interval to estimate the difference between the proportion of Central Valley and Bay Area residents who approve of the California Legislature A. (-0.224, -0.136) B. (o.o94, 0.266) C. (-o.266, -0.094) D. O (o.136, 0.224)

Explanation / Answer

Proportion of Central valley residents who approve of the California legislature = 68/200 = 0.34 (p1)

Proportion of Bay area residents who approve of the California legislature = 156/300 = 0.52 (p2)

Given that Standard error of (p1 - p2) = 0.044

Confidence interval of difference between proportions = (p1 - p2) +- z0.025 Standard error of (p1 - p2)

= (0.34-0.52)+-1.96*0.044

= (-0.266 , -0.094)

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