Question

Two samples are taken from different populations with the following sample means, sizes, and standard deviations:

Sample 1: Mean = 35, Size = 60, Standard Deviation = 4
Sample 2: Mean = 37, Size = 58, Standard Deviation = 2
Find an 89% confidence interval estimate of the difference between the means of the two populations. Round answers to the nearest hundredth.
a. (0.72, 2.28)
b. (1.08, 2.16)
c. (1.48, 2.76)
d. (2.04, 2.76

Answer 1

To find the 89% confidence interval estimate of the difference between the means of two populations, we can use the formula CI = (X1 - X2) ± Z * sqrt((s1^2/n1) + (s2^2/n2)). Substituting the given values, the 89% confidence interval estimate of the difference between the means of the two populations is (-2.69, 1.31), rounded to the nearest hundredth.

Step-by-step explanation:

To find the 89% confidence interval estimate of the difference between the means of two populations, we can use the formula:

CI = (X1 - X2) ± Z * sqrt((s1^2/n1) + (s2^2/n2))

where CI is the confidence interval, X1 and X2 are the sample means, s1 and s2 are the standard deviations, n1 and n2 are the sample sizes, and Z is the Z-value corresponding to the desired confidence level.

Substituting the given values:

CI = (35 - 37) ± 1.645 * sqrt((4^2/60) + (2^2/58))

= -2 ± 1.645 * sqrt(0.1067 + 0.0689)

= -2 ± 1.645 * sqrt(0.1756)

= -2 ± 1.645 * 0.4188

= -2 ± 0.68821

Therefore, the 89% confidence interval estimate of the difference between the means of the two populations is (-2.69, 1.31), rounded to the nearest hundredth.