Computing confidence intervals for a mean with summary data
This tutorial covers the steps for computing one-sample confidence intervals 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 confidence intervals for a mean with raw 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 in a bottle be 64.05 ounces 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 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, choose Confidence interval for μ. Be 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.