Question

1. A farmer wants to test the effectiveness of a pest control method in allowing strawberry blooms to yield marketable strawberries. Of a random sample of 100 blooms, 77 yield marketable strawberries. Is this evidence that two thirds or more of all blooms grown with this pest control method end up as marketable strawberries? The 95% large-sample confidence interval for the proportion of blooms that yield marketable strawberries is:

A)  0.77 ± 0.042.

B)  0.77 ± 0.082.

C) 0.77 ± 0.0034.

D). 0.77 ± 0.0017.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 77 / 100 = 0.77

1 - = 1 - 0.770 = 0.23

Z/2 = 1.96

A 95% confidence interval for population proportion p is ,

  Z / 2 * (( * (1 - )) / n)

0.77 1.645 * (((0.77 * 0.23) / 100)

0.77 0.082

option B) is correct