Researchers sample 3000 households concerning tv shows they watch. Based on the sample 15% reported watching...

Researchers sample 3000 households concerning tv shows they watch. Based on the sample 15% reported watching 60 minutes. What is the 95% confidence interval for the proportion of all Americans that watch 60 minutes

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Expert Solution

Solution :

Given that,

n = 3000

= 15%=0.15

1 - = 1 - 0.15 = 0.85

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Margin of error = E = Z_{/ 2} * $\sqrt$ (( * (1 - )) / n)

= 1.96 * ( $\sqrt$ ((0.15 * 0.85) / 3000 = 0.01278

A 95 % confidence interval for proportion p is ,

- E < P < + E

0.15 - 0.01278 < p < 0.15 + 0.01278

0.13722 < p < 0.16278

The 95% confidence interval for the proportion of all Americans that watch 60 minutes p is :

( 0.13722, 0.16278)

Sun, Jul 15, 9:40 PM

milcah answered 7 months ago

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