Question

onsider a random sample of size n=144yielded p^=0.76. Which of the following is a 90% confidence interval for p?

Select one:

a. (0.230, 0.850)

b. (0.341, 0.872)

c. (0.478, 0.971)

d. (0.701, 0.819)

Answer 1

Solution :

Given that,

n = 144

= 0.760

1 - = 1 - 0.760 = 0.240

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z_0.05 = 1.645

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

= 1.645 * (((0.760 * 0.240) / 144)

= 0.059

A 90 % confidence interval for population proportion p is ,

- E < P < + E

0.760- 0.059 < p < 0.760 + 0.059

0.701 < p < 0.819

The 90% confidence interval for the population proportion p is : ( 0.701 , 0.819)

Answer d ) is correct.