Because refunds are paid more quickly on tax returns that are fi led electronically, the Commissioner of the Internal Revenue Service was wondering whether refunds due on returns fi led by mail were smaller than those due on returns fi led electronically. Looking only at returns claiming refunds, a sample of 17 fi led by mail had an average refund of $563, and a standard deviation of $378. The average refund on a sample of 13 electronically fi led returns was $958, and the sample standard deviation was $619. At α = 0.01, do these data support the commissioner’s speculation?

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