Question

How many women must be randomly selected to estimate the mean weight of women in one age group. We want 90% confidence that the sample mean is within 3.7 lb of the population mean, and the population standard deviation is known to be 28 lb.

Answer 1

Answer: the required sample size = 155

Step-by-step explanation:

If the standard deviation of the prior study is known, then the formula to compute required sample size:

$n=(\frac{z^*\times\sigma}{E})^2$, where E = Margin of error, z* = Critical value, $\sigma$ =  populion standard deviation.

Given: E = 3.7 , $\sigma=28$

Critical value for 90% confidence = 1.645

Required sample size: $n=(\frac{1.645\times28}{3.7})^2$

$n=(12.4486486486)^2\approx155$

Hence, the required sample size = 155