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q2s - √ 900 × 47 = 14 1 ≈ 14 The SE of the percentages...

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Math 127B, Quiz 2 Solutions Thursday, February 3rd, 2011 Name: Recitation Section: Ten minutes. Calculators allowed. 20 points maximum. 1. A simple random sample of 900 draws will be made from the box 2 million 0 ’s, 1 million 1 ’s . (a) Give an estimate for the percentage of 1’s in the sample. [ 6 points] Solution The estimate is given by 1 3 × 900 = 300. The percentage is 300 / 900 33 . 3%. (b) By how much is the estimate off from the true percentage. [ 10 points] Solution The SD of the box is given by 0 . 33 × 0 . 67 0 . 47. The Se of the number of 1s is
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Unformatted text preview: √ 900 × . 47 = 14 . 1 ≈ 14. The SE of the percentages is 14 900 × 100% = 1 . 55 ≈ 1 . 6%. (c) How much is the estimate off from the true percentage for the following box: 2 billion ’s, 1 billion 1 ’s . Explain, without recalculating everything. [ 4 points] Solution Since the population in both cases is quite large in relation to the sample the accuracy depends on the sample size. So the SE here is also about 1.6%. 1...
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