Question

Find the necessary confidence interval for a population mean for the following values. (round your answers to two decimal places.) = 0.05, n = 87, x = 66.6, s2 = 2.28

Answer 1

To find the necessary confidence interval for a population mean, we can use the sample mean, standard deviation, and sample size. With the given information, we can calculate the confidence intervals for 95 percent and 90 percent level of confidence.

Step-by-step explanation:

In order to find the confidence interval, we need the sample mean, x, and the estimated standard error of the mean (EBM). The formula for calculating the EBM is:

EBM = 1.96 * (s / √n)

where s is the standard deviation and n is the sample size.

Plugging in the given values, we can calculate the necessary confidence intervals:

For a 95 percent confidence interval:

EBM = 1.96 * (2.28 / √87) ≈ 0.501

Confidence interval = x ± EBM = 66.6 ± 0.501 = (66.1, 67.1)

For a 90 percent confidence interval:

EBM = 1.645 * (2.28 / √87) ≈ 0.41

Confidence interval = x ± EBM = 66.6 ± 0.418 = (66.2, 67.0)