# Select the analysis options for 2 Proportions

Stat > Basic Statistics > 2 Proportions > Options

Specify the confidence level for the confidence interval, specify the hypothesized difference, define the alternative hypothesis, or specify whether to use the pooled estimate of the proportion.

## Confidence level

In Confidence level, enter the level of confidence for the confidence interval.

Usually, a confidence level of 95% works well. A 95% confidence level indicates that, if you take 100 random samples from the population, the confidence intervals for approximately 95 of the samples will contain the population difference.

For a given set of data, a lower confidence level produces a narrower confidence interval, and a higher confidence level produces a wider confidence interval. The width of the interval also tends to decrease with larger sample sizes. Therefore, you may want to use a confidence level other than 95%, depending on your sample size.
• If your sample size is small, a 95% confidence interval may be too wide to be useful. Using a lower confidence level, such as 90%, produces a narrower interval. However, the likelihood that the interval contains the population difference decreases.
• If your sample size is large, consider using a higher confidence level, such as 99%. With a large sample, a 99% confidence level may still produce a reasonably narrow interval, while also increasing the likelihood that the interval contains the population difference.

## Hypothesized difference

Enter a value in Hypothesized difference. The hypothesized difference defines your null hypothesis. Think of this value as a target value or a reference value. For example, a company tests whether the proportion of defective parts from a new supplier is different by 0.01 (1%) from the proportion from the current supplier (pnew – pcurrent = 0.01).

## Alternative hypothesis

From Alternative hypothesis, select the hypothesis that you want to test:

Difference < hypothesized difference

Use this one-sided test to determine whether the difference between the population proportions of sample 1 and sample 2 is less than the hypothesized proportion, and get an upper bound. This one-sided test has greater power than a two-sided test, but it cannot detect whether the difference is greater than the hypothesized difference.

For example, an engineer uses this one-sided test to determine whether the difference between the proportions of defective parts from two grades of material is less than 0. This one-sided test has greater power to detect whether the difference in proportions of defective parts is less than 0, but it cannot detect whether the difference is greater than 0.

Difference ≠ hypothesized difference

Use this two-sided test to determine whether the difference in population proportions differs from the hypothesized difference, and to get a two-sided confidence interval. This two-sided test can detect differences that are less than or greater than the hypothesized difference, but it has less power than a one-sided test.

For example, a bank manager tests whether the proportion of customers who have savings accounts differs at two locations. Because any difference in the proportions is important, the manager uses this two-sided test to determine whether the proportion at one location is greater than or less than the other location.

Difference > hypothesized difference

Use this one-sided test to determine whether the difference between the population proportions of sample 1 and sample 2 is greater than the hypothesized difference, and to get a lower bound. This one-sided test has greater power than a two-sided test, but it cannot detect whether the difference is less than the hypothesized difference.

For example, a logistics analyst uses this one-sided test to determine whether the difference in the proportions of on-time packages for two locations is greater than 0. This one-sided test has greater power to detect whether the difference in on-time deliveries is greater than 0, but it cannot detect whether the difference is less than 0.

For more information on selecting a one-sided or two-sided alternative hypothesis, go to About the null and alternative hypotheses.

## Test method

From Test method, select the method for estimating the proportion. When the samples are large and equal, the default method of estimating the proportions separately is preferred. If the samples are equal but small the default method is less accurate.

When you select Use the pooled estimate of the proportion, the Hypothesized difference must be equal to 0 and Minitab does not calculate a confidence interval based on the pooled estimate of the proportion. Minitab still displays a confidence interval, but it is calculated based on the default method of estimating the proportions separately.

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