Conducting hypothesis tests for a mean with raw data

This tutorial covers the steps for conducting one-sample hypothesis tests in StatCrunch. To begin, load the Apple Juice Bottles data set, which will be used throughout this tutorial. This data set comes from "Statistics: Informed Decisions Using Data" by Michael Sullivan. The Apple Juice (oz) column contains the amount in ounces in each of 22 bottles taken as a random sample from a manufacturer's assembly line. The filling machine is not precise which makes the amount of juice vary from bottle to bottle. This tutorial will cover using one-sample T methods for this raw data set with individual measurements. A very similar approach can be used for one-sample Z methods which are appropriate for large sample sizes and/or known standard deviation. To compute one-sample results using the sample mean, sample standard deviation and sample size, see Conducting hypothesis tests for a mean with summary data.

Performing a one-sample hypothesis test

Each bottle's label states it contains 64 ounces of apple juice. The manufacturer requires that the mean amount of juice per bottle to actually be 64.05 ounces in order 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 Data menu option. Select the Apple Juice (oz) column. 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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