Question

To receive full credit on the confidence intervals, you must show each of the following: a. The critical value (3 points) b. The margin of error (round answers to at least hundredths) (3 points) c. The minimum and maximum numbers of the interval (3 points each) To receive full credit on the interpretations, you must include information about the specific problem. When finding the sample size, remember to round all answers up to the next highest whole number Show all work for partial credit!

Answer 1

Solution :

Given that,

n = 56

x = 41

a ) Point estimate = sample proportion = $\hat p$ = x / n = 41 / 56 = 0.732

1 - $\hat p$ = 1 - 0.732 = 0.268

b) At 90% confidence level the z is,

$\alpha$ = 1 - 90%

$\alpha$ = 1 - 0.90 = 0.10

$\alpha$/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 * ($\sqrt$((0.732 * 0.268 ) / 56 )

= 0.097

A 90% confidence interval for population proportion p is ,

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

0.732 - 0.097 < p < 0.732 + 0.097

0.635 < p < 0.829

The 90% confidence interval for the population proportion p is : 0.64, 0.83 ( round to at least hundredths )