Question

please within decimal format only

In a study of 407 nonprofits nationwide, 87 indicated that turnover has been the biggest employment challenge at their organization. Complete parts (a) through (c). a. Construct a 95% confidence interval or the population proportion o nonprofits that in cate turnover as the i gest employment challenge at en,organization □SaS□ Type integers or decimals. Round to three decimal places as needed.)

Answer 1

$95\%~C.I.~for~population~proportion,~\pi~of~nonprofits~that~indicate~turnover\\ as~the~biggest~employment~challenge~at~their~organization:\\ \left(\hat{\pi}-Z_{0.025}\sqrt{\frac{\hat{\pi}(1-\hat{\pi})}{407}},~\hat{\pi}+Z_{0.025}\sqrt{\frac{\hat{\pi}(1-\hat{\pi})}{407}} \right )=(0.174,~0.254)\\ where,~\hat{\pi}=87/407=0.214,~Z_{0.025}=1.96$