# Question: An economist was interested in studying the impact of the

An economist was interested in studying the impact of the recession on dining out, including drive thru meals at fast food restaurants. A random sample of forty-eight families of four with discretionary incomes between \$300 and \$400 per week indicated that they reduced their spending on dining out by an average of \$31.47 per week, with a sample standard deviation of \$10.95. Another random sample of 42 families of five with discretionary incomes between \$300 and \$400 per week reduced their spending on dining out by an average \$35.28 per week, with a sample standard deviation of \$12.37. Assume that the distributions of reductions in weekly dining-out spendings for the two groups have the same population standard deviation.
a. Construct a 90% confidence interval for the difference in the mean weekly reduction in dining out spending levels for the two populations.
b. Using a 5% significance level, can you conclude that the average weekly spending reduction for all families of four with discretionary incomes between \$300 and \$400 per week is less than the average weekly spending reduction for all families of five with discretionary incomes between \$300 and \$400 per week?

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• CreatedAugust 25, 2015
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