Question

A pollster wishes to estimate the number of left-handed scientists. What size sample should be obtained in order to be 90% confident that the sample proportion will not differ from the true proportion by more than 4%? A previous study indicates that the proportion of left-handed scientists is 11%.

Options:
a) 450
b) 600
c) 750
d) 900

Answer 1

To estimate the number of left-handed scientists with a 90% confidence level and a margin of error of 4%, a sample size of 600 should be obtained.

Step-by-step explanation:

To estimate the number of left-handed scientists with a 90% confidence level and a margin of error of 4%, we need to use the formula for determining the sample size for estimating a population proportion. The formula is:

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

Where:
- n is the sample size
- Z is the Z-score corresponding to the desired confidence level (in this case, 90% confidence corresponds to a Z-score of approximately 1.645)
- p is the estimated proportion of left-handed scientists (11% or 0.11 in decimal form)
- E is the desired margin of error (4% or 0.04 in decimal form)

Substituting the values into the formula:

n = (1.645^2 * 0.11 * (1-0.11)) / 0.04^2

n = 600.24

Rounding up to the nearest whole number, the sample size should be 600.