Question

Wviknding to the American Time Use Survey. Amereate slepp an weerage of 7.g9 hours each day with a unhierd devietige of 2.35 hours. Let 1 be the sitrage of a randorm sample of americans. What sample iize will yive the standard devietion of x ecual to 6 , it heunt Rowand the solution up to the nearest whele numbtes, if macievary

Answer 1

To find the sample size needed for a standard deviation of 6, use the formula n = (Z * sigma / E)^2, where n is the sample size, Z is the Z-value for the desired confidence level, sigma is the population standard deviation, and E is the desired margin of error. For a 95% confidence level and a population standard deviation of 2.35, the sample size needed is approximately 12.

Step-by-step explanation:

In order to find the sample size needed to yield a standard deviation of 6, we can use the formula n = (Z * sigma / E)^2, where n is the sample size, Z is the Z-value for the desired confidence level, sigma is the population standard deviation, and E is the desired margin of error.

First, we need to find the Z-value for the desired confidence level. Let's assume a 95% confidence level, which corresponds to a Z-value of 1.96.

Then, we can substitute the known values into the formula: n = (1.96 * 2.35 / 6)^2. Calculating this expression gives n = 11.58. Since we need to round up to the nearest whole number, the sample size that will give a standard deviation of approximately 6 is 12.