EXAMPLE 7.17 Planning a New Smart Shopping Cart Study

As part of Example 7.10 (pages 381–382), we calculated a 95% confidence interval for the mean difference in spending when shopping with and without real-time feedback. The 95% margin of error was roughly $2.70. Suppose that a new study is being planned and the desired margin of error is $1.50. How many shoppers per group do we need?

The sample standard deviations in Example 7.10 were $6.59 and $6.85. To be a bit conservative, we’ll guess that the two population standard deviations are both $7.00. To compute an initial , we replace with . This results in

We round up to get . The following table summarizes the margin of error for this and some larger values of .

The requirement is first satisfied when . In SAS, we’d perform these calculations using the command

proc power;

  twosamplemeans CI=diff stddev=7 halfwidth=1.5

  probwidth=0.50 npergroup=.;

run;

402

This sample size is almost 3.5 times the sample size used in Example 7.10. The researcher may not be able to recruit this large a sample. If so, we should consider a larger desired margin of error.