Question

Dr. Ashby is studying the heart rate of adult men. Preliminary data suggests that the standard deviation of heart rates for adult men is σ = 7.5 σ=7.5sigma, equals, 7, point, 5 beats per minute (bpm). He plans on taking a sample of n nn men to construct a 99 % 99%99, percent confidence interval for the mean heart rate. He wants the margin of error to be no more than 3 bpm 3 bpm3, start text, space, b, p, m, end text.

Answer 1

Answer:

n=42 adult men

Step-by-step explanation:

-The minimum sample size to get a desired margin of error, E is calculated using the formula:

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

-Given that $\sigma=7.5, \ \ E=3\ , \ z_{0.005}=2.58$, we can substitute to solve for n in the above formula:

$n\geq (\frac{z\sigma}{E})^2\\\\\therefore n=(\frac{z_{\alpha/2}\sigma}{E})^2\\\\=(\frac{2.58\times7.5}{3})^2\\\\=41.6025\approx42$

Hence, the desired minimum sample size, n is 42 adult men.