Conducting hypothesis tests for a mean with summary data

This tutorial covers the steps for conducting one-sample hypothesis tests with summary information in StatCrunch. For this example, a random sample of 22 apple juice bottles from a manufacturer's assembly line has a sample mean of 64.01 ounces of juice and a sample standard deviation of 0.05. The filling machine is not precise which makes the amount of juice vary from bottle to bottle. This example comes from "Statistics: Informed Decisions Using Data" by Michael Sullivan. This tutorial covers using one-sample T methods with the sample size and the summary information from the sample consisting of the sample mean and sample standard deviation. A very similar approach can be used for the one-sample Z methods with summary data. To compute one-sample results using the corresponding raw data set with individual measurements, see Computing hypothesis tests for a mean with raw data.

Performing a one-sample hypothesis test with summary

Each bottle's label states it contains 64 ounces of apple juice. The manufacturer requires that the mean amount of juice in a bottle be 64.05 ounces to decrease the chance of a bottle being under the 64 ounce threshold by random chance. Given the manufacturers concern about under filling bottles, conduct a test to determine if the mean amount per bottle may be less than the target of 64.05 ounces. To compute the appropriate one-sample T hypothesis test results, choose the Stat > T Stats > One Sample > With Summary menu option. Enter 64.01 for the Sample mean, 0.05 for the Sample std. dev., and 22 for the Sample size. Under Perform, the Hypothesis test for μ is selected by default. Enter 64.05 for the null value of the population mean, μ. For this example, change the alternative hypothesis to < to test if the mean amount of apple juice in a bottle is actually lower than the 64.05 ounce standard. Click Compute! to view the hypothesis test results. The output table provides various statistics from this test including the test statistic and the P-value.

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