q7s - that use paper and pencil. The percentage in...

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Math 127B, Quiz 7 Thursday, March 24th, 2011 Name: Recitation Section: Ten minutes. Calculators allowed. 20 points maximum. 1. An experiment is performed to decide whether calculators help students to work word problems. The subjects are a group of 500 thirteen-year-olds in a certain school district. All the subjects work the same problem. Half of them are chosen at random and allowed to use a calculator; the others do the problem with paper and pencil. In the calculator group, 18 get the right answer; in the pencil-and-paper group, 59 get the right answer. Is this difference real or just chance? [ 20 points] Solution This is a randomized control experiment. The null hypothesis is that there is no difference between the percentage who use calculators and those
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Unformatted text preview: that use paper and pencil. The percentage in calculator group is 18 / 250 100 = 7 . 2%, in the pencil-and-paper group it is 59 / 250 100 = 23 . 6%. The SE for the number in the two groups is 250 . 072 . 928 = 4 . 08. The SE for the percentage is 4 . 08 / 250 100 = 1 . 63%. The SE for the number is 250 . 236 . 764 = 6 . 71. The SE for percentage is 6 . 71 / 250 100 = 2 . 68%. The SE for the dierence is 1 . 63 2 + 2 . 68 2 = 7 . 22%. The test statistic is z = 23 . 6-7 . 2 7 . 22 = 2 . 27. The P-value is 1%. This is highly signicant, so reject the null the dierence is real. 1...
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