Question

Excessive commericals and advertising	18%
Game delys,including penalty flags	24%
Off-field image problems with domestic violence	18%
National anthem protest	30%
Cord-Cutting	6%

what is the 90 95 and 99 confidence intervals sample size is 114

Answer 1

sample mean proportion = (0.18 + 0.24 + 0.18 + 0.3 + 0.06)/5 = 0.96/5

Sample proportion ($\hat{p}$) = 0.192
Sample size (n) = 114
Confidence interval(in %) = 90
z @ 90% = 1.645
Since we know that
$\\Confidence\; interval = \hat{p} \pm z_{\alpha}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \\Required\; confidence\; interval = (0.192-1.645\sqrt{\frac{0.192(1-0.192)}{114}}, 0.192+1.645\sqrt{\frac{0.192(1-0.192)}{114}})$
Required confidence interval = (0.192-0.0607, 0.192+0.0607)
Required confidence interval = (0.1313, 0.2527)

Confidence interval(in %) = 95
z @ 95% = 1.96
Since we know that
$\\Confidence\; interval = \hat{p} \pm z_{\alpha}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \\Required\; confidence\; interval = (0.192-1.96\sqrt{\frac{0.192(1-0.192)}{114}}, 0.192+1.96\sqrt{\frac{0.192(1-0.192)}{114}})$
Required confidence interval = (0.192-0.0723, 0.192+0.0723)
Required confidence interval = (0.1197, 0.2643)

Confidence interval(in %) = 99
z @ 99% = 2.576
Since we know that
$\\Confidence\; interval = \hat{p} \pm z_{\alpha}\sqrt{\frac{\hat{p}(1-\hat{p})}{n}} \\Required\; confidence\; interval = (0.192-2.576\sqrt{\frac{0.192(1-0.192)}{114}}, 0.192+2.576\sqrt{\frac{0.192(1-0.192)}{114}})$
Required confidence interval = (0.192-0.0951, 0.192+0.0951)
Required confidence interval = (0.0969, 0.2871)
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