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# We need to minimize 24 n a 24 n b this is 0163 for

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), we need to minimize . 24 n A + . 24 n B . This is 0.163 for choice (1) and 0.107 for choice (2). Choice (2) has smaller width. (b) By looking at the expression above, the CI width is minimized when 1 n A + 1 n B is as small as possible with n A + n B = 100. Based on part(a), the width is smaller for the values of n A and n B that are closer together. Thus the ’natural’ conjecture is that the CI width can be minimized if n A = n B = 50. This is the correct answer. It is primarily for this reason that most scientific studies comparing 2 (or more) groups have equal sample sizes. Grade Distribution 90-99:22 80-89:41 70-79:26 median = 79 60-69:17 50-59:13 below: 8
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