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 choicesn

Answer 1

Therefore, the animal scientist needs a sample size of at least 274 heifers.

To solve this problem

we can use the following formula:

n = \frac{p(1-p)}{Z^2/4(e)^2}

where:

The sample size is denoted by n.

The percentage of heifers who need assistance is denoted by p (0.20).

The desired confidence level's z-score, Z, is 1.96 for a 90% confidence level.

The margin of error, or e, is 0.05.

Entering the values yields:

N equals \frac{0.2(1-0.2)}.{1.96^2/4(0.05)^2}

n equals 273.18.

In order to estimate the percentage of heifers who require assistance with a margin of error of 0.05 and a confidence level of 0.90, the animal scientist needs a sample size of at least 274 heifers.