Determine the Sample Size Necessary for Estimating the Population Mean within a Specified Margin of Error
-$\mathrm { E } = 4 , \sigma = 35 \text {, } ( 1 - \alpha ) = 0.90$
A) 208
B) 207
C) 4
D) 295

Question

Quizplus · Accepted Answer

To determine the sample size necessary for estimating the population mean within a specified margin of error, we use the formula $n = \left( \frac{Z \sigma}{E} \right)^2$, where $n$ is the sample size, $Z$ is the Z-score corresponding to the confidence level, $\sigma$ is the population standard deviation, and $E$ is the margin of error. For a 90% confidence level, the Z-score is approximately 1.645. Plugging in the values: $n = \left( \frac{1.645 \times 35}{4} \right)^2 \approx 207.4$. Since the sample size must be a whole number, we round up to the nearest whole number, which is 208.

Determine the Sample Size Necessary for Estimating the Population Mean E=4,σ=35, (1−α)=0.90\mathrm { E } = 4 , \sigma = 35 \text {, } ( 1 - \alpha ) = 0.90E=4,σ=35, (1−α)=0.90

Determine the Sample Size Necessary for Estimating the Population Mean $\mathrm { E } = 4 , \sigma = 35 \text {, } ( 1 - \alpha ) = 0.90$