Find the necessary sample size.
-The weekly earnings of students in one age group are normally distributed with a standard deviation of 10 dollars. A researcher wishes to estimate the mean weekly earnings of students in
This age group. Find the sample size needed to assure with 95 percent confidence that the sample
Mean will not differ from the population mean by more than 2 dollars.
A)10
B)7
C)20
D)97

Question

Find the necessary sample size.
-The weekly earnings of students in one age group are normally distributed with a standard deviation of 10 dollars. A researcher wishes to estimate the mean weekly earnings of students in
This age group. Find the sample size needed to assure with 95 percent confidence that the sample
Mean will not differ from the population mean by more than 2 dollars. 
A)10
B)7
C)20
D)97

Quizplus · Accepted Answer

To find the necessary sample size for estimating the mean with a specific margin of error (E), confidence level (Z), and population standard deviation (σ), we use the formula: $n = \left(\frac{Z\sigma}{E}\right)^2$. For a 95% confidence level, Z is approximately 1.96. Given σ = 10 dollars and E = 2 dollars, substituting these values gives $n = \left(\frac{1.96 \times 10}{2}\right)^2 = 96.04$, which rounds up to 97 to ensure the sample mean is within 2 dollars of the population mean with 95% confidence.

Find the Necessary Sample Size