Question

A pollster wishes to estimate the number of left-handed scientists. What size sample should be obtained to be 90% confident that the sample proportion will not differ from the true proportion by more than 4%?

A) 600
B) 675
C) 700
D) 750

Answer 1

To estimate the number of left-handed scientists with a 4% margin of error and 90% confidence, you need a sample size of 675.

Step-by-step explanation:

To determine the sample size required to estimate the proportion of left-handed scientists with a 4% margin of error and 90% confidence, we need to use the formula for sample size determination for proportions. The formula is:

n = (Z^2 * p * (1-p)) / E^2

Where:

• n is the required sample size
• Z is the z-score corresponding to the desired confidence level
• p is the estimated proportion
• E is the desired margin of error as a proportion

In this case, we are given that the margin of error is 4% or 0.04, and we want a 90% confidence level. The z-score corresponding to a 90% confidence level is approximately 1.645. We don't have an estimated proportion, so we can assume a worst-case scenario where p = 0.5, since this will give us the maximum required sample size. Plugging in the values, we get:

n = (1.645^2 * 0.5 * (1-0.5)) / 0.04^2 = 675

The required sample size is 675, so the answer is option B) 675.