Select the analysis options for 1 Proportion

Stat > Basic Statistics > 1 Proportion > Options

Specify the confidence level for the confidence interval, define the alternative hypothesis, or specify the method for the test and confidence interval.

In This Topic

Confidence level
Alternative hypothesis
Method

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 cover the population parameter.

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 covers the population proportion 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 covers the population proportion.

Alternative hypothesis

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

Proportion < hypothesized proportion

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

For example, an engineer uses this one-sided test to determine whether the proportion of defective parts is less than 0.001 (0.1%). This one-sided test has greater power to determine whether the proportion is less than 0.001, but it cannot detect whether the proportion is greater than 0.001.

Proportion ≠ hypothesized proportion

Use this two-sided test to determine whether the population proportion differs from the hypothesized proportion, and to get a two-sided confidence interval. A two-sided test can detect differences that are less than or greater than the hypothesized value, 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 this year differs from last year's proportion, 0.57 (57%). Because any difference from last year's proportion is important, the manager uses this two-sided test to determine whether this year's proportion is greater than or less than last year's proportion.

Proportion > hypothesized proportion

Use this one-sided test to determine whether the population proportion is greater than the hypothesized proportion, and to get a lower bound. This one-sided test has greater power than a two-sided test, but it cannot detect whether the population proportion is less than the hypothesized proportion.

For example, a quality analyst uses this one-sided test to determine whether the proportion of acceptable electrical switches is greater than 0.98. This one-sided test has greater power to determine whether the proportion is greater than 0.98, but it cannot determine whether the proportion is less than 0.98.

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

Method

From Method, select the method to calculate the hypothesis test and confidence interval.

Adjusted Blaker (Exact): By default, Minitab uses the adjusted Blaker exact method because the confidence intervals are more precise than the Clopper-Pearson exact method. Intervals from the adjusted Blaker exact method are nested. This property means that confidence intervals with higher confidence levels contain confidence intervals with lower confidence levels. For example, an exact, two-sided Blaker 95% confidence interval contains the corresponding 90% confidence interval.; When you select Proportion < hypothesized proportion or Proportion > hypothesized proportion and the Method is Adjusted Blaker (Exact), the analysis uses the Clopper-Pearson exact method because the adjusted Blaker exact method is for the hypothesis Proportion ≠ hypothesized proportion. The Clopper-Pearson exact method is usually excessively conservative for two-sided intervals such that the actual confidence level of the interval is greater than the specified confidence level. For one-sided intervals, the Clopper-Pearson method is less conservative than for the two-sided case.
Wilson-score: The Wilson-score method is a reasonable choice for many practical applications. The actual confidence level of the Wilson-score interval is often below the nominal confidence level that you specify in the analysis. Use the continuity correction so that actual confidence level is at least the nominal confidence level in the analysis.
Agresti-Coull: Many statistics textbooks teach the Agresti-Coull interval. The Agresti-Coull interval does not use iterative calculations, so the results are easier for students to calculate manually than the adjusted Blaker interval or the Wilson-score interval. The Agresti-Coull interval has the same midpoint as the Wilson-score confidence interval without a continuity correction. The Agresti-Coull interval contains the Wilson-score interval, which makes the Agresti-Coulll interval more conservative than the Wilson-score interval.
Normal approximation (Web app): Many statistics textbooks teach the Wald normal approximation interval. The Wald interval does not use iterative calculations, so the results are easier for students to calculate manually than the adjusted Blaker interval or the Wilson-score interval. The midpoint of the Wald interval is the observed probability.