Z-Procedures

Calculating the Test Statistic

The Problem

Example #351: Let us estimate the difference in means between two populations using a confidence interval to indicate our uncertainty. To do this, we collect data from each of the two populations. The data from population 1 are:

37, 38, 43, 44, 38, 42, 58, 70, 30, 35, 54, 64, 51, 7, 29, 58, 21, 24, 16, 9, 16, 44, 82, 44, 69, 58, 31, 28, 44, 58, 41, 54, 41, 27, 27, 38, 20, 45, 15, 62, 56

The data from population 2 are:

35, 31, 34, 48, 24, 42, 46, 44, 24, 54, 58, 39, 33, 42, 29, 59, 28, 44, 44, 35, 36, 52, 46, 18, 43, 39, 56, 42, 52, 54, 39, 39, 50, 37, 54, 38, 46, 36, 37, 44, 41, 48, 42, 49, 47, 24, 40, 55, 44, 63, 36, 56, 32, 36

In addition to these data, we also know two important things. First, the data are generated from independent Normal processes; that is, the data in each sample come from independent Normal distributions. Second, we know that the population variances are σ²1 = 289 and σ²2 = 121.

With this information, calculate the endpoints of the symmetric 95% confidence interval for the difference in population means, μ1 − μ2.

Information given:

To summarize the above, the values of import are:

Summary statistics from the problem
\( \bar{x}_1 \) =
\( \bar{x}_2 \) =
   
\( \sigma_1 \) =
\( \sigma_2 \) =
   
\( n_1 \) =
\( n_2 \) =
   
\( \alpha \) =

Calculate these values yourself then hover your mouse over the grey spaces to see if you calculated them correctly.

Your Answer

In the box below, please enter the two endpoints of the 95% confidence interval for the population mean, then click on the “Check your answer!” button. Please round your answer to the ten-thousandths place.

95% Confidence Bounds: (, )

Make sure the lower limit is less than the upper limit.

Assistance

Show Formula

Show Solution

Show the R Code

Show the Excel Code

© Ole J. Forsberg, Ph.D. 2024. All rights reserved.   .