Part 6 Review solutions

Part 6 Review solutions - Review of Part VI 451 Review of...

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Review of Part VI 451 Review of Part VI – Learning About the World 1. Crawling. a) H 0 : The mean age at which babies begin to crawl is the same whether the babies were born in January or July. µµ Jan July Jan July =− = () or 0 H A : There is a difference in the mean age at which babies begin to crawl, depending on whether the babies were born in January or July. Jan July Jan July ≠− or 0 Independent groups assumption: The groups of January and July babies are independent. Randomization condition: Although not specifically stated, we will assume that the babies are representative of all babies. 10% condition: 32 and 21 are less than 10% of all babies. Nearly Normal condition: We don’t have the actual data, so we can’t check the distribution of the sample. However, the samples are fairly large. The Central Limit Theorem allows us to proceed. Since the conditions are satisfied, it is appropriate to model the sampling distribution of the difference in means with a Student’s t -model, with 43.68 degrees of freedom (from the approximation formula). We will perform a two-sample t -test. The sampling distribution model has mean 0, with standard error: SE y y Jan July .. . −= + 708 32 691 21 1 9596 22 . The observed difference between the mean ages is 29.84 – 33.64 = – 3.8 weeks. Since the P - value = 0.0590 is fairly low, we reject the null hypothesis. There is some evidence that mean age at which babies crawl is different for January and June babies. June babies appear to crawl a bit earlier than July babies, on average. Since the evidence is not strong, we might want to do some more research into this claim. b) H 0 : The mean age at which babies begin to crawl is the same whether the babies were born in April or October. Apr Oct Apr Oct = or 0 H A : There is a difference in the mean age at which babies begin to crawl, depending on whether the babies were born in April or October. Apr Oct Apr Oct or 0 The conditions (with minor variations) were checked in part a. t yy SE y y t t Jan July Jan July = −− ≈− 0 38 0 1 9596 194 . . .
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452 Part VI Learning About the World Since the conditions are satisfied, it is appropriate to model the sampling distribution of the difference in means with a Student’s t -model, with 59.40 degrees of freedom (from the approximation formula). We will perform a two-sample t -test. The sampling distribution model has mean 0, with standard error: SE y y Apr Oct () .. . −= + 621 26 729 44 1 6404 22 . The observed difference between the mean ages is 31.84 – 33.35 = – 1.51 weeks. Since the P - value = 0.3610 is high, we fail to reject the null hypothesis. There is no evidence that mean age at which babies crawl is different for April and October babies. c) These results are not consistent with the researcher’s claim. We have slight evidence in one test and no evidence in the other. The researcher will have to do better than this to convince us!
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This note was uploaded on 05/20/2008 for the course STAT 50 taught by Professor Weinstein during the Spring '08 term at Harvard.

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Part 6 Review solutions - Review of Part VI 451 Review of...

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