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A brokerage firm is said to provide both brokerage services and "research" if, in addition to buying and selling securities for its clients, the firm furnishes clients with advice about the value of securities, information on economic factors and trends, and portfolio strategy. The Securities and Exchange Commission (SEC) has been studying brokerage commissions charged by both "research" and "nonresearch" brokerage houses.

A random sample of 255 transactions at nonresearch firms is collected as well as a random sample of 300 transactions at research firms. These samples reveal that the difference between the average sample percentage of commission at research firms and the average percentage of commission in the nonresearch sample is 2.54%. The standard deviation of the research firms' sample is 0.85%, and that of the nonresearch firms is 0.64%.

Give a 95% confidence interval for the difference in the average percentage of commissions in research versus nonresearch brokerage houses. In each of the following problems assume that the two populations of interest are normally distributed with equal variance. Assume independent random sampling from the two populations.

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