Question

A population has standard deviation o = 17.2.

Part 1 of 2
(a) How large a sample must be drawn so that a 99.8% confidence interval for u will have a margin of error equal to 3.8?
Round the critical value to no less than three decimal places.
Round the sample size up to the nearest integer.
A sample size of
3.8.
is needed to be drawn in order to obtain a 99.8% confidence interval with a margin of error equal to

Answer 1

In order to obtain a 99.8% confidence interval with a margin of error of 3.8, a sample size of 397 must be drawn.

Step-by-step explanation:

To determine the sample size needed for a 99.8% confidence interval with a margin of error of 3.8, we need to find the critical value corresponding to a 99.8% confidence level. The critical value is found using the z-score formula: Z = invnorm(1 - (1 - confidence level)/2) = invnorm(1 - (1- 0.998)/2) = invnorm(0.999). Rounding this value to three decimal places gives us a critical value of 3.090.

The margin of error (E) is given by the formula E = Z * (o / sqrt(n)), where o is the standard deviation of the population, and n is the sample size. Rearranging the formula to solve for n, we have n = (Z * o / E)^2. Plugging in the values, we get n = (3.090 * 17.2 / 3.8)^2. Rounding up to the nearest integer, the sample size needed is 397.