Statistics in a Modern World 800
Solutions to Practice Final Exam

1. (c) observational study
2.  
   1. source: American Journal of Clinical Nutrition (study done by FDA)
   2. researchers:? (doctors presumably assessed whether or not women had the genetic abnormality; perhaps other doctors assessed Down syndrome)
   3. individuals: mothers
   4. measurements: presence or absence of genetic abnormality, Down syndrome or not
   5. setting:? (hospital and/or doctor's office?)
   6. compare women with the genetic abnormality to women without
   7. those with abnormality are 2.6 times likelier to have Down syndrome child
3. (c) more than 1000 (otherwise we wouldn't have enough cases of Down syndrome, which occurs in 1 out of 600)
4. (b) possible interacting variables ("something else has to help trigger the devastating condition")
5. (a) explanatory variable
6. (b) bargraph
7.  
   1. (i) invalid (not measuring what they're supposed to)
   2. (ii) unreliable (measurements not consistent)
8.  
   1. median is between 15th and 16th values, or 116.5
   2. (ii) fairly symmetric
   3. (ii) mean about equal to median
   4. 8th value, or 106
9.  
   1. z=(110-100)/8=1.25; proportion with z above +1.25 = proportion with z below -1.25 = .11
   2. shortest 5% have z=-1.64, so observed value = 100-1.64(8) = 86.88
10.  
    1. 3.6 + .97(55) = 56.95
    2. (ii) older, because the slope +.97 is positive
11.  
    1. 2
    2. 4
    3. 1
    4. 5
    5. 3
12.  
    1. null hypothesis: no relationship between drinking and smoking; alternative hypothesis: there IS a relationship
    2. expected counts are 162, 108, 198, 132
    3. compared counts are 2, 3, 1.6, 2.5
    4. chi-squared statistic = 2+3+1.6+2.5 = 9.1
    5. p-value less than .05, since chi-squared is greater than 3.84
    6. yes, because we reject the null hypothesis with a small p-value
13. (calculations are in terms of thousands of miles)
    1. null hypothesis: mean duration = 22; alternative hypothesis: mean duration less than 22
    2. z= (21.8-22)/(1.2/10) = -1.67
    3. p-value = probability of z below -1.67 = .05
    4. (iii) results are borderline
14.  
    1. .33 + .20 = .53
    2. 1 - .53 = .47
15.  
    1. no: .34(.05) is not equal to .03
    2. .34 + .05 - .03 = .36
16.  
    1. 1/2 * 1/2 * 1/2 * 1/2 = 1/16
    2. (iii) a total of 2 boys and 2 girls can happen in several ways: BBGG or BGBG or BGGB or GBGB or GBBG or BBGG
17. 500(.9) - 1500(.1) = 300
18. (b) getting a queen (most general)
19. (g) conservatism
20. (a) anchoring
21. (e) optimism
22. (b) availability
23.  
    1. .01(.8) = .008
    2. .99(.1) = .099
    3. .008 + .099 = .107
24.  
25.  
    1. .5
    2. square root of .5(1-.5)/81 = .056
    3. approximately normal
    4. .444 and .556
    5. .388 and .612
    6. .332 and .668
26.  
    1. 52/81 = .64
    2. SE = square root of .64(1-.64)/81 = .053; interval is .64 plus or minus 2(.053) = (.53, .75)
27.  
    1. null hypothesis: proportion of women = .5; alternative hypothesis: proportion of women > .5
    2. SE = square root of .5(1-.5)/81 = .056, so z= (.64-.5)/.056 = 2.5
    3. p-value = probability of z above 2.5 = probability of z below -2.5 = .005
    4. (ii) small p-value means reject the null and conclude the alternative is true
28.  
    1. 68.2 plus or minus 2(2.7/square root of 200) = (67.8, 68.6)
    2. 95% of the time, an interval constructed by this method will in fact contain the unknown population mean. Alternatively, I am 95% confident that mean height of all men is between 67.8 and 68.6.
29. (a) combine results if studies have quite similar conditions
30. (b) keep results separate if studies have quite different conditions

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