Question

Geri Dumi- Quiz 4C x+ STAZ023 TR 1230-545 n5a5) Spg 2019 a92) Quiz 4 Chapter 7 7 of 8 me Remaining 13056 A random sample of 25 individuals working in a large city indicated that S2 are dissatished with their-arking ear diam Ba ed upon t-come. 8% confidence interval for the proportion of all individuals in this city who are dissatisfied with their working conditions. Then complete the table below Carry your intermediate computations to at least three decimal places. Round your answers to two decimal places. (If necessary, consult a list of formulas.) What is the lower limit of the 95% confidence interval? | what is the upper limit of the 95% confidence interval? Worked Example

Answer 1

$Let~p=proportion~of~individuals~who~are~dissatisfied.\\ \hat{p}=estimate~of~p=52/250=0.208000 \\ Z_{0.025}=1.96\\ 95\%~C.I.~for~p~is\\ \left(\hat{p}-Z_{0.025}\sqrt{\frac{\hat{p}(1-\hat{p})}{250}},~\hat{p} +Z_{0.025}\sqrt{\frac{\hat{p}(1-\hat{p})}{250}} \right )=(0.159421, 0.263647)\\ Lower~limit=0.16~(rounded~2~decimal~places)\\ Upper~limit=0.26~(rounded~2~decimal~places)$