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

n=42 adult men

Explanation:

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

`n\geq( (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 ((z\sigma)/(E))^2\\\\\therefore n=((z_(\alpha/2)\sigma)/(E))^2\\\\=((2.58*7.5)/(3))^2\\\\=41.6025\approx42`

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