Statistics in a Modern World 800
Solutions to Practice Final Exam
 (c) observational study

 source: American Journal of Clinical Nutrition (study done by FDA)
 researchers:? (doctors presumably assessed whether or not women had the
genetic abnormality; perhaps other doctors assessed Down syndrome)
 individuals: mothers
 measurements: presence or absence
of genetic abnormality, Down syndrome or not
 setting:? (hospital and/or doctor's office?)
 compare women with the genetic abnormality to women without
 those with abnormality are 2.6 times likelier to have Down syndrome child
 (c) more than 1000 (otherwise we wouldn't have enough cases of Down
syndrome, which occurs in 1 out of 600)
 (b) possible interacting variables ("something else has to help trigger
the devastating condition")
 (a) explanatory variable
 (b) bargraph

 (i) invalid (not measuring what they're supposed to)
 (ii) unreliable (measurements not consistent)

 median is between 15th and 16th values, or 116.5
 (ii) fairly symmetric
 (ii) mean about equal to median
 8th value, or 106

 z=(110100)/8=1.25; proportion with z above +1.25 = proportion with
z below 1.25 = .11
 shortest 5% have z=1.64, so observed value = 1001.64(8) = 86.88

 3.6 + .97(55) = 56.95
 (ii) older, because the slope +.97 is positive

 2
 4
 1
 5
 3

 null hypothesis: no relationship between drinking and smoking; alternative
hypothesis: there IS a relationship
 expected counts are 162, 108, 198, 132
 compared counts are 2, 3, 1.6, 2.5
 chisquared statistic = 2+3+1.6+2.5 = 9.1
 pvalue less than .05, since chisquared is greater than 3.84
 yes, because we reject the null hypothesis with a small pvalue
 (calculations are in terms of thousands of miles)
 null hypothesis: mean duration = 22; alternative hypothesis: mean
duration less than 22
 z= (21.822)/(1.2/10) = 1.67
 pvalue = probability of z below 1.67 = .05
 (iii) results are borderline

 .33 + .20 = .53
 1  .53 = .47

 no: .34(.05) is not equal to .03
 .34 + .05  .03 = .36

 1/2 * 1/2 * 1/2 * 1/2 = 1/16
 (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
 500(.9)  1500(.1) = 300
 (b) getting a queen (most general)
 (g) conservatism
 (a) anchoring
 (e) optimism
 (b) availability

 .01(.8) = .008
 .99(.1) = .099
 .008 + .099 = .107


 .5
 square root of .5(1.5)/81 = .056
 approximately normal
 .444 and .556
 .388 and .612
 .332 and .668

 52/81 = .64
 SE = square root of .64(1.64)/81 = .053; interval is .64 plus or minus
2(.053) = (.53, .75)

 null hypothesis: proportion of women = .5; alternative hypothesis:
proportion of women > .5
 SE = square root of .5(1.5)/81 = .056, so z= (.64.5)/.056 = 2.5
 pvalue = probability of z above 2.5 = probability of z below 2.5
= .005
 (ii) small pvalue means reject the null and conclude the alternative
is true

 68.2 plus or minus 2(2.7/square root of 200) = (67.8, 68.6)
 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.
 (a) combine results if studies have quite similar conditions
 (b) keep results separate if studies have quite different conditions
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