Question

Out of a random sample of 1019 American adults, 642 of them believe that upper-income Americans are paying too little in taxes. (Gallup, April 11, 2017) Find a 90% confidence interval for the proportion of all American adults who believe that up too little in taxes. Make sure to draw a conclusion in plain English. 2. per-income Americans are paying FYI: Trump's tax plan would is expected to reduce taxes for upper-income Americans (CNN Money April 24, 2017).

Answer 1

Solution :

Given that,

n = 1019

x = 642

$\hat p$ = x / n = 642 / 1019 = 630

1 -$\hat p$ = 1 - 0.630=0.370

At 90% confidence level the z is ,

$\alpha$ = 1 - 90% = 1 - 0.90 = 0.10

$\alpha$ / 2 = 0.10 / 2 = 0.05

Z_$\alpha$/2 = Z_0.05 = 1.645

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

= 1.645 * ($\sqrt$((0.630*0.370/1049) = 0.025

A 90 % confidence interval for population proportion p is ,

$\hat p$ - E < P <$\hat p$ + E

0.630 - 0.025 < p < 0.630 + 0.025

0.605 < p < 0.655

The 90% confidence interval for the population proportion p is : (0.605 , 0.655 )