Question

A population has standard deviation 17.9 .

Part 1 of 2 (a) How large a sample must be drawn so that a 99.8% confidence interval for mew will have a margin of error equal to 4.8 Round the critical value to no less than three decimal places. Round the sample size up to the nearest integer.

A sample size of ____ is needed to be drawn in order to obtain a 99.8% confidence interval with a margin of error equal to 4.8 .

Part 2 of 2 (b) If the required confidence level were 99%, would the necessary sample size be larger or smaller? , _______ because the confidence level is _______ .

Answer 1

a)

The following information is provided,
Significance Level, α = 0.002, Margin or Error, E = 4.8, σ = 17.9

The critical value for significance level, α = 0.002 is 3.09.

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 = (3.09 * 17.9/4.8)^2
n = 132.78

Therefore, the sample size needed to satisfy the condition n >= 132.78 and it must be an integer number, we conclude that the minimum required sample size is n = 133
Ans : Sample size, n = 133

b)

smaller because confidenc elevel is decrease