EXAMPLE 7.11 Does Real-time Feedback Influence Spending?

For the grocery spending study described in Example 7.10, we want to see if there is a difference in average spending between the group of participants that had real-time feedback and the group that did not. For a formal significance test, the hypotheses are

The two-sample test statistic is

The -value for the two-sided test is . Software gives the approximate -value as 0.0410 and uses 94.63 as the degrees of freedom.

For the second approximation, the degrees of freedom are equal to 47. Because there is no row for , we use the closest value of in the table that is less than 47. Comparing with the entries in Table D for 40 degrees of freedom, we see that lies between and . The data do suggest that consumers on a budget will spend more when provided with real-time feedback .