Question

Use the given information to find the minimum sample size required to estimate an unknown population mean μ.

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 2.0 lb of the population mean, and the population standard deviation is known to be 27 lb.

Answer 1

Solution :

Given that,

Population standard deviation = = 27

Margin of error = E = 2

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

Z_/2 = Z _0.05 = 1.645

sample size = n = (Z_/2* / E) ²

n = (1.645 * 27 / 2)²

n = 493.17

n = 494

Sample size = 494