Question

The ages of a group of 147 randomly selected adult females have a standard deviation of 17.9 years. Assume that the ages of female statistics students have less variation than ages of females in the general population, so let σ=17.9 years for the sample size calculation. How many female statistics student ages must be obtained in order to estimate the mean age of all female statistics students? Assume that we want 99% confidence that the sample mean is within one-half year of the population mean. Does it seem reasonable to assume that the ages of female statistics students have less variation than ages of females in the general population?1. )The required sample size is ____ (Round to the nearest whole number)2. )Does it seem reasonable to assume that the ages of female statistics students have less variation than ages of females in the general population?A. No, because statistics students are typically older than people in the general population.B. No, because there is no age difference between the population of statistics students and the general population.C.Yes, because statistics students are typically younger than people in the general population.D. Yes, because statistics students are typically older than people in the general population.

Answer 1

1. Given:

Standard deviation: σ = 17.9

Confidence = 99%

Now, formula to find the margin of error is:

$E=z\frac{\sigma}{\sqrt{n}}$

Where:

E is margin of error

z is critical value at confidence level

σ is standard deviation

n is required sample size

Since that the sample mean is within one-half year of the population mean. So:

E = 0.5

We have that z value at 99% Confidence level is z = 2.576.

We clear n in the formula:

$n=(\frac{z\sigma}{E})^2$

Substitute the values:

$n=(\frac{2.576\cdot17.9}{0.5})^2=8504.67$

Round to the nearest whole number is 8505

Answer: The required sample size is 8505

2. Statistics students are younger than people in the general population. Therefore:

Answer: C.