Question

In a recent poll of 900 randomly selected​ adults, a​ president's approval rating stood at 52%.

a) Find the 90% confidence interval as a true proportion.

(____,_____)

b) Based on the confidence interval, can the null hypothesis be rejected?

__________ the null hypothesis

1. rejected

2. fail to reject

Answer 1

Solution :

Given that,

(a)

n = 900

Point estimate = sample proportion = = 0.52

1 - = 0.48

Z_/2 = Z _0.05 = 1.645

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.645 * (((0.52 * 0.48) / 900)

= 0.027

A 90% confidence interval for population proportion p is ,

- E < p < + E

0.52 - 0.027 < p < 0.52 + 0.027

0.493 < p < 0.547

(0.493 , 0.547)

The 90% confidence interval for the population proportion p is : (0.493 , 0.547)

(b)

fail to reject the null hypothesis .

Because 0.5 is in the confidence interval .