Confidence Interval for the Difference Between Means Example 9.9 Husband and Wife Reactions to Sales Presentations at Stevens Honda-Olds Confidence Interval for the Difference Between Means

Objective To use StatPro’s paired-sample procedure to find a confidence interval for the mean difference between husbands’ and wives’ ratings of sales presentations.

Background Information The Steven Honda-Olds automobile dealership often sells to husband/wife pairs. The manager would like to know if the sales presentation is viewed any more or less favorably by the husbands than the wives. If it is, then some new training might be recommended for its salespeople. To check for differences, a random sample of husbands and wives are asked (separately) to rate the sales presentation on a scale of 1 to 10, 10 being the most favorable.

AUTO.XLS The data is included in this file. What can the manager conclude from the data?

Analysis There are two ways to perform this analysis. The first way is to use the One-Sample Analysis. To begin create a copy of the Data sheet and call it OneSample. Then manually form a new variable in Column D called Difference by entering the formula =B4-C4 and copy it down Column D. Next, use the One-Sample procedure to get the output. The sample mean difference is 1.629 and a 95% confidence interval for this difference extends from 1.057 to 2.200.

One-Sample Analysis of Differences

Analysis -- continued The second way will perform this analysis more efficiently. Again, to begin make a copy of the DataSheet and call it Paired. Use the Paired-Sample Analysis menu item. The results are exactly the same as before; this is because the Paired-Sample procedure performs a one-sample analysis on the differences - and it saves you the work of creating the differences.

Paired-Sample Analysis

Boxplots Boxplots are shown for the husband’s and wife’s scores as well as for the differences. The differences boxplot is more useful. We can see that the sample mean difference is positive, but even more importantly, we see that the vast majority of husband scores are greater than the corresponding wife scores. There is little doubt that husbands react more favorably to the sales presentations than their wives.

Side-by Side Boxplots

Single Boxplot of Differences

Two-Sample Analysis? What would have resulted if we used the two-sample analysis for this example. Using the two-sample procedure, results shown on next slide, we obtained a confidence interval for the mean difference that extends from 0.895 to 2.362 which is somewhat wider than the paired-sample procedure. When the two-sample procedure is used on data that is more appropriate for the paired-sample, we see that the standard error of the difference tends to be larger, and the resulting confidence interval tends to be wider.

Paired-Sample Procedure Why is the paired -sample procedure appropriate here? It’s not because husbands and wives come in pairs but it is because they tend to react similarly to one another. The correlation between husband’s and wife’s scores is 0.442. This is far from perfect correlation but large enough to warrant using the paired sample procedure.