Question

An animal scientist wants to estimate the proportion of heifers that require assistance when giving birth to their first calves. Based on previous research, the animal scientist believes that the proportion of heifers that require assistance is 0.20. How large of a sample does the animal scientist need in order to obtain an estimate of p that is correct to within 0.05 with probability equal to 0.90?

Group of answer choices

n = 174 heifers

n = 6 heifers

n = 271 heifers

n = 105 heifers

Answer 1

Solution :

Given that,

= 0.20

1 - = 1 - 0.20 = 0.80

margin of error = E = 0.05

At 90% confidence level z

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z_{0.05 = 1.645}

Sample size = n = (Z_/2 / E)² * * (1 - )

= (1.645 / 0.05)² * 0.20* 0.80

=174

Sample size = 174