Computing confidence intervals for a mean with raw data
This tutorial covers the steps for computing confidence intervals 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 Computing confidence intervals for a mean with summary data.
Calculating a confidence interval for the mean
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. To create a confidence interval for the population mean, choose the Stat > T Stats > One Sample > With Data menu option. Select the Apple Juice (oz) column. Under Perform, choose Confidence interval for μ. By default StatCrunch has a value of 0.95 for the Level input which will produce a 95% confidence level for the population mean, μ. Changing this value to 0.99 would produce a 99% confidence interval. Leave the Level at the default 0.95 and click Compute!. The results below show a 95% confidence interval for the mean amount in one of the manufacturer's bottles with "L. Limit" representing the lower limit and "U. Limit" representing the upper limit of this confidence interval.