Question

8. A group of 121 Hobbits are interviewed and only 15% of them would be excited to go an unexpected journey. Build an 88% confidence interval for the true proportion of Hobbits that would be excited to go an unexpected journey. [Round the final values to two decimal places.] (12 points)

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = 0.15

1 - = 1 - 0.15 = 0.85

Z/2 = 1.555

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

= 1.555 * (((0.15 * 0.85) / 121)

Margin of error = E = 0.05

A 88% confidence interval for population proportion p is ,

- E < p < + E

0.15 - 0.05 < p < 0.15 + 0.05

0.10 < p < 0.20

88% C . I. = (0.10 , 0.20)