Z-Procedures

Calculating the Confidence Interval

The Problem

Example # 449: Estimate the difference in success rates between two populations using a confidence interval to indicate uncertainty. To estimate this difference, we collect data. The data are a series of “Success” and “Failure” values. For sample 1, the data are

“Failure”, “Success”, “Success”, “Failure”, “Failure”, “Failure”, “Failure”, “Success”, “Success”, “Failure”, “Failure”, “Failure”, “Failure”, “Failure”, “Success”, “Failure”, “Failure”, “Failure”, “Success”, “Failure”, “Failure”, “Failure”, “Failure”, “Failure”, “Failure”, “Success”, “Failure”, “Failure”, “Success”, “Success”, “Failure”, “Success”, “Failure”, “Failure”, “Failure”, “Success”, “Failure”, “Failure”, “Success”, “Failure”

For sample 2, the data are

“Failure”, “Failure”, “Success”, “Failure”, “Success”, “Failure”, “Success”, “Success”, “Success”, “Success”, “Failure”, “Failure”, “Failure”, “Failure”, “Success”, “Failure”, “Success”, “Success”, “Failure”, “Failure”, “Failure”, “Failure”, “Failure”, “Success”, “Failure”, “Failure”, “Failure”, “Failure”, “Failure”

With this information, calculate the endpoints of the symmetric 99% confidence interval.

Information given:

To summarize the above, the values of import are:

Summary statistics from the problem
\( x_1 \) =
\( x_2 \) =
  
\( n_1 \) =
\( n_2 \) =
  
\( \hat{p}_1 \) =
\( \hat{p}_2 \) =
  
\( \alpha \) =

Note that there is no value given for the hypothesized difference p0. This is because confidence intervals are based solely on the data, and not on any hypothesized values.

It may be helpful if you calculate these values yourself. Once you have, you can check your answers by hovering 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 99% confidence interval for the difference in population proportions, then click on the “Check your answer!” button. Please round your answer to the ten-thousandths place.

99% Confidence Bounds: (, )

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

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