A farmer wants to test the effectiveness of a pest control m

A farmer wants to test the effectiveness of a pest control method in allowing strawberry blooms to yield marketable strawberries. In a pilot study of a random sample of 100 blooms, 77 yield marketable strawberries. What sample size should be used for a future study to ensure that the margin of error is less than 5 percentage points, 95% of the time?

Solution

A farmer wants to test the effectiveness of a pest control method in allowing strawberry blooms to yield marketable strawberries. In a pilot study of a random sample of 100 blooms, 77 yield marketable strawberries. What sample size should be used for a future study to ensure that the margin of error is less than 5 percentage points, 95% of the time?

Sample size

P=77/10000.77

For 95%, z=1.96

d=0.05 ( margin of error)

Sample size = (z²*p*(1-p))/d²

= (1.96²*0.77*0.23)/0.05²

= 272.1389

The sample size required= 273