Question

1. Weights of women in one age group are normally distributed with a standard deviation σ of 21 lb. A researcher wishes to estimate the mean weight of all women in this age group. How large a sample must be drawn in order to be 95 percent confident that the sample mean will not differ from the population mean by more than 2.2 lb? First, what formula or test would be used to calculate that number?

	A.
	B.	TInterval
	C.
	D.

2. How large a sample must be drawn in order to be 95 percent confident that the sample mean will not differ from the population mean by more than 2.2 lb?

Answer 1

The following information is provided,
Significance Level, α = 0.05, Margin or Error, E = 2.2, σ = 21

The critical value for significance level, α = 0.05 is 1.96.

The following formula is used to compute the minimum sample size required to estimate the population mean μ within the required margin of error:
n >= (zc *σ/E)^2
n = (1.96 * 21/2.2)^2
n = 350.03

Therefore, the sample size needed to satisfy the condition n >= 350.03 and it must be an integer number, we conclude that the minimum required sample size is n = 351
Ans : Sample size, n = 351 or 350