Hypothesis Tests and Confidence Intervals in Minitab Express

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1 Hypothesis Tests and Confidence Intervals in Minitab Express Open Minitab Express. You may enter your data as you would in Microsoft Excel (or any other spreadsheet), or you can copy and paste the data from another application (like Excel). Example: t-test. A student weighed ten samples of ½ of hazelnut coffee from a local coffee house. The results, in pounds, are given in the table shown. We ll investigate whether the sample provides evidence that the average ½ pound of coffee is actually less than ½ pound. Copy the data and paste it into Minitab. A normal probability plot and the result of an Anderson-Darling test (p = ) suggest that t-procedures are OK to use. Click the Statistics tab. You ll see a large number of options for statistical analysis. Weights For hypothesis tests and confidence intervals involving 1-sample, click on One-Sample For tests about a population mean, select 1-sample t-test. For tests about a population proportion, select 1-sample proportion test. For the example using weights of ½ pounds of coffee, we want a 1-sample t-test. A dialog box will open like this: Your data can be either summary data (mean, SD) or raw data. Use the pull-down menu to select which you have. In this example, we have the raw data, so select Sample data in a column.

2 Highlight the column that contains the variable data and then select that variable by clicking the arrow. Next, check the box: Perform hypothesis test. In the Hypothesized mean box, enter the hypothesized mean (that s the value you re comparing the sample mean to). In the example, the coffee bags should be 0.5 pounds. Click on the Options tab. This allows you to choose the direction of the alternative hypothesis and set the confidence interval level. Use the pull-down menu Alternative hypothesis to pick the direction of the alternative hypothesis. For this example, we want Mean < hypothesized value. Unless you have a 2-sided test, you can ignore the Confidence level box. In the output window, you ll see results of the hypothesis test. You will see the mean, standard deviation and standard error of the sample Below, you find the p-value is , so we don t reject the null hypothesis. The sample doesn t provide enough evidence to support the claim that the average weight of ½ pound bags of this coffee is actually less than ½ pound.

3 Hypothesis Tests for a Population Proportion in Minitab Express Example: proportion test. The standard treatment for a disease works in 67.5% of all patients. A new treatment is proposed. Is it better? A clinical trial of n = 100 randomly selected patients is conducted in which 77 people are cured. Is the new treatment better? Test at the 1% significance level. Click the Statistics tab. Click on One-Sample and then click on Proportion. A dialog box will appear like this: From the pull-down menu, select Summarized data. Enter the number of events and the number of trials. Then check the Perform hypothesis test box and enter the hypothesized proportion. Next, click the Options tab. From the Alternative hypothesis pull-down menu, select the appropriate alternative hypothesis. In this example, the claim is that the proportion of cures with the new treatment will be higher, so select Proportion > hypothesized value For Method, use the default Exact. Press OK.

4 The results of the hypothesis test appear in the output window. Minitab gives you a summary of the sample data. Below the descriptive statistics you will see the results of the hypothesis test including the p-value Since the p-value is less than 0.05 (p = ), the conclusion we draw from the hypothesis test is that the proportion of cures with the new treatment is significantly higher than 67.5%. Confidence Interval for a Population Mean in Minitab Express To construct a confidence interval for a mean (for example, the coffee data), from the Statistics tab, click One Sample and select 1-sample t-test as you did for the hypothesis test. Again, you will see a dialog box like this: Use the pull-down menu to select which kind of data you have (raw data or summaries). In this example, we have the raw data, so select Sample data in a column. Since we re not doing a hypothesis test, leave the Perform hypothesis test box unchecked.

5 Click on the Options tab. This allows you to choose the direction of the alternative hypothesis and set the confidence interval level. Use the pull-down menu Alternative hypothesis to pick the direction of the alternative hypothesis. For a confidence interval, we always want Mean hypothesized value. Finally, in the Confidence level box, you can either enter a confidence level or select from the pulldown menu. Click OK. The results (including the confidence interval) will appear in the output window. Notice that in this case, the hypothesized mean is contained in the confidence interval. This gives additional support to the conclusion of the hypothesis test that the average weight of the ½ pound bags of coffee is not less than ½ pound. Confidence Interval for a Population Proportion in Minitab Express Click on One-Sample and then click on Proportion. From the pull-down menu, select Summarized data. Enter the number of events and the number of trials. Leave the Perform hypothesis test box blank

6 Next, click the Options tab. Use the pull-down menu Alternative hypothesis to pick the direction of the alternative hypothesis. For a confidence interval, we always want Mean hypothesized value. In the Confidence level box, you can either enter a confidence level or select from the pull-down menu. For Method, use the default Exact. Press OK. The results (including the confidence interval) will appear in the output window. So, we are 95% confident that for all people in the population, the cure rate for the new treatment is between 67.5% and 84.8%. Notice that in this case, the hypothesized proportion, 0.675, is contained in the confidence interval. This seems to contradict the hypothesis test that said the proportion of cures with the new treatment is significantly higher than 67.5%. This phenomenon will occur when performing a 1-sided hypothesis test for which the p-value is fairly close to the level of significance. For our example, the p-value was which is close to If the p-value is small (compared to the significance level), this result will generally not happen.