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Part 7 Review solutions

# Part 7 Review solutions - 514 Part VII Inference When...

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514 Part VII Inference When Variables Are Related Review of Part VII – Inference When Variables Are Related 1. Genetics. H 0 : The proportions of traits are as specified by the ratio 1:3:3:9. H A : The proportions of traits are not as specified. Counted data condition: The data are counts. Randomization condition: Assume that these students are representative of all people. Expected cell frequency condition: The expected counts (shown in the table) are all greater than 5. Under these conditions, the sampling distribution of the test statistic is χ 2 on 4 – 1 = 3 degrees of freedom. We will use a chi-square goodness-of-fit test. Trait Observed Expected Residual = ( Obs – Exp ) ( ) Obs Exp 2 Component = ( ) Obs Exp Exp 2 Attached, noncurling 10 7.625 2.375 5.6406 0.73975 Attached, curling 22 22.875 – 0.875 0.7656 0.03347 Free, noncurling 31 22.875 8.125 66.0156 2.8859 Free, curling 59 68.625 – 9.625 92.6406 1.35 5.01 χ 2 5 01 = . . Since the P -value = 0.1711 is high, we fail to reject the null hypothesis. There is no evidence that the proportions of traits are anything other than 1:3:3:9. 2. Tableware. a) Since there are 57 degrees of freedom, there were 59 different products in the analysis. b) 84.5% of the variation in retail price is explained by the polishing time. c) Assuming the conditions have been met, the sampling distribution of the regression slope can be modeled by a Student’s t -model with (59 – 2) = 57 degrees of freedom. We will use a regression slope t -interval. For 95% confidence, use t 57 2 0025 . , or estimate from the table t 50 2 009 . . b t SE b n 1 2 1 2 49244 2 0025 0 1416 2 21 2 78 ± × ( ) = ± × . ( . ) . ( . , . ) d) We are 95% confident that the average price increases between \$2.21 and \$2.78 for each additional minute of polishing time.

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Review of Part VII 515 3. Hard water. a) H 0 : There is no linear relationship between calcium concentration in water and mortality rates for males. β 1 0 = ( ) H A : There is a linear relationship between calcium concentration in water and mortality rates for males. β 1 0 ( ) b) Assuming the conditions have been satisfied, the sampling distribution of the regression slope can be modeled by a Student’s t -model with (61 – 2) = 59 degrees of freedom. We will use a regression slope t -test. The equation of the line of best fit for these data points is: Mortality Calcium ˆ . ( ) = 1676 3 23 , where mortality is measured in deaths per 100,000, and calcium concentration is measured in parts per million. The value of t = – 6.73. The P -value of less than 0.0001 means that the association we see in the data is unlikely to occur by chance. We reject the null hypothesis, and conclude that there is strong evidence of a linear relationship between calcium concentration and mortality. Towns with higher calcium concentrations tend to have lower mortality rates. c) For 95% confidence, use t 59 2 001 . , or estimate from the table t 50 2 009 . .
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