Question

Given two independent random samples with the following results: n1=13x‾1=180s1=21   n2=9x‾2=163s2=30 Use this data to find the 99% confidence interval for the true difference between the population means. Assume that the population variances are equal and that the two populations are normally distributed.

Step 1 of 3: Find the point estimate that should be used in constructing the confidence interval.

Step 2 of 3: Find the margin of error to be used in constructing the confidence interval. Round your answer to six decimal places.

Step 3 of 3: Construct the 99%99% confidence interval. Round your answers to the nearest whole number.

Answer 1

Given that,

For sample 1 : n1 = 13, x1-bar = 180 and s1 = 21

For sample 2 : n2 = 9, x2-bar = 163 and s2 = 30

Assume that the population variances are equal.

Pooled variance is,

Step 1) The point estimate for (μ1 - μ2) is,

Step 2) Degrees of freedom = 13 + 9 - 2 = 20

t-critical value at significance level of 0.01 with 20 degrees of freedom is,

Excel Command : = TINV (0.01, 20) = 2.845339

The margin of error (E) is,

=> Margin of error = 30.835672

Step 3) The 99% confidence interval for (μ1 - μ2) is,

Therefore, the 99% confidence interval is, (-14, 48)