CH10 exercises solutions

CH10 exercises solutions - X X X X X X X X X X X X X X X X...

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X X X X X X X X X X X X X X X X X AP Statistics Solutions to Packet 10 X Introduction to Inference Estimating with Confidence Tests of Significance Making Statistical Sense of Significance Inference as a Decision X X X X X X
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2 HW #12 1 – 3, 5 10.1 POLLING WOMEN A New York Times poll on women’s issues interviewed 1025 women randomly selected from the US, excluding Alaska and Hawaii. The poll found that 47% of the women said they do not get enough time for themselves. (a) The poll announced a margin of error of 3 percentage points for 95% confidence in its conclusions. What is the 95% confidence interval for the percent of all adult women who think they do not get enough time for themselves? 44% to 50% (b) Explain to someone who knows no statistics why we can’t just say that 47% of all adult women do not get enough time for themselves. We do not have information about the whole population; we only know about a small sample. We expect our sample to give us a good estimate of the population value, but it will not be exactly correct. (c) Then explain clearly what “95% confidence” means. The procedure used gives an estimate within 3 percentage points of the true value in 95% of all samples. 10.2 NAEP SCORES Young people have a better chance of full-time employment and good wages if they are good with numbers. How strong are the quantitative skills of young Americans of working age? One source of data is the National Assessment of Educational Progress (NAEP) Young Adult Literacy Assessment Survey, which is based on a nationwide probability sample of households. The NAEP survey includes a short test of quantitative skills, covering mainly basic arithmetic and the ability to apply it to realistic problems. Scores on the test range from 0 to 500. For example, a person who scores 233 can add the amounts of two checks appearing on a bank deposit slip; someone scoring 325 can determine the price of a meal from a menu; a person scoring 375 can transform a price in cents per ounce into dollars per pound. Suppose that you give the NAEP test to a SRS of 840 people from a large population in which the scores have mean 280 and standard deviation s = 60. The mean x of the 840 scores will vary if you take repeated samples. (a) Describe the shape, center, and spread of the sampling distribution of x . What guarantees this? 60 840 280, N    840 < 10% population of young Americans of working age standard deviation formula works We can assume the sampling distribution is approximately normal because n = 840 is large enough that we can use CLT
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3 (b) Sketch the normal curve that describes how x varies in many samples from this population. Mark its mean and the values 1, 2, and 3 standard deviations on either side of the mean. (c) According to the 68-95-99.7% rule, about 95% of all the values of x fall within 2 4.2 s ± = of the mean of the curve. What is the missing number? Call it m for “margin of error”. Sketch the region from the mean minus m to the mean plus m on the axis of your sketch.
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CH10 exercises solutions - X X X X X X X X X X X X X X X X...

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