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spring2008stat201exam3-version1KEY

spring2008stat201exam3-version1KEY - Stat 201 Exam 3 Spring...

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Stat 201 Exam 3 Spring 2008 Version 1 KEY Page 1 of 10 1. In order to estimate the proportion, p , of current smokers among all Pennsylvania residents, suppose a random sample of 100 residents was chosen, and 36 of them were found to be smokers. (a) Compute as necessary and report the value of the sample statistic (i.e., the ‘point estimate’ of the parameter of interest). Also, give its appropriate symbol. [2 pts for symbol; 3 pts for value] .36 100 36 = “pee-hat p ˆ = 0.36 (symbol ) (numerical value) [2 pts] [3 pts] (b) Construct a 95% confidence interval for the proportion of smokers. [Show work.] [5 pts] n ) p (1 p z p ˆ ˆ ˆ - ± ° – or – Using z=2: 100 .36) .36(1 2 .36 - ± 2(.048) .36 ± = .096 .36 ± = = .45) , (.26 [some rounding ok] Using z=1.96: 100 .36) .36(1 1.96 .36 - ± 1.96(.048) .36 ± = .094 .36 ± = .45) , (.26 [some rounding ok] (c) Report the margin of error. [3 pts] .096 or .094 (depending which z was used) [exercise 1 continues on next page]
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Stat 201 Exam 3 Spring 2008 Version 1 KEY Page 2 of 10 (d) Suppose that, ten years ago, the proportion of smokers among all Pennsylvania residents was 40%. Based on your confidence interval, is there evidence that the proportion has changed from ten years ago? Give the best answer, as follows: [4 pts total] Choose the appropriate response: The answer to this part depends on the interval, as follows: If .40 in the interval ° “no” (not changed) (this is the intended answer) If .40 out side the interval ° “yes” (changed) (i) yes, there is evidence the proportion has changed (ii) no, there isn’t evidence that the proportion changed (this is the intended answer) Because [select the appropriate reason]: (i) You checked to see if 0 . 36 is in the interval. (ii) You checked to see if 36 is in the interval. (iii) You checked to see if 1 . 96 is in the interval. (iv) You checked to see if 0 . 40 is in the interval. (v) You checked to see if 0 . 04 is in the interval. (vi) You checked to see if 4 is in the interval. (vii) You checked to see if . 05 is in the interval. (viii) You checked to see if the margin of error is in the interval. (ix) You checked to see if zero is in the interval. (x) There were 36 smokers in the sample.
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Stat 201 Exam 3 Spring 2008 Version 1 KEY Page 3 of 10 2. Hemoglobin is a protein in red blood cells that carries oxygen from the lungs to the body tissues. Having too little hemoglobin can be bad. The hemoglobin level for healthy adults follows a Normal distribution, with mean of 12 grams per unit of blood, and standard deviation 6 1 . = σ grams per unit of blood. To test whether poverty is associated with abnormally low hemoglobin, suppose researchers test a random sample of 50 impoverished adults, and find an average of 11 . 3 grams per unit of blood for the sample. The researchers want to test the hypothesis that the mean hemoglobin level for impoverished adults is lower than the known healthy level. Construct the hypotheses by selecting the most appropriate choice for each blank: [1 pt each] Null Hypothesis: _________________ = _________________ circle the best choice from (a) circle the best choice from (b) Alternative Hypothesis: _________________ ______ _________________ circle the best choice from (c) circle the circle the best choice from (e) best choice from (d) (a) : (i) p (ii) p ˆ (iii) μ (test for mean)
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