Statistics in a Modern World 800
Solutions to Exam 4

1. (a) (-7,8) because it contains 0
2. (b) (1,4) and (2,5) because they have the most overlap
3.  
   1. mean is population mean 3.5
   2. standard error is 1.7/square root of 25 = .34
   3. normal (or bell-shaped)
   4. mean plus or minus 1 standard error: between 3.16 and 3.84
   5. now standard error is 1.7/square root of 100 = .17: between 3.33 and 3.67
4.  
   1. standard error is square root of (.3)(.7)/933 = .015; 95% confidence interval is sample proportion plus or minus 2 standard errors, or (.27,.33)
   2. no, because interval is way below .5
   3. (i) wider: dividing by larger sample gives larger margin of error
   4. (iii) inaccurate: the sample is biased
5. (b) very small p-value provides very strong evidence, but it may be a weak relationship
6.   (c) sample must be random and large enough
7.  
   1. (ii) equal to 40
   2. (iii) greater than 40
   3. 20/square root of 1600 = .5
   4. (41-40)/.5 = 2
   5. probability of z greater than or equal to 2, same as probability of z less than or equal to -2, .02 or .025
   6. yes because the p-value is small
   7. (i) yes because the sample size is large
8.  
   1. (iii) two-sample z test
   2. (iv) chi-squared test
   3. (i) z test about a proportion
   4. (ii) z test about a mean
9. (a) one-sided test for a mean
10. .08/2 = .04
11. (b) combine into meta-analysis
12. (b) do NOT tend to die earlier (that's why it's a paradox!)
13. Extra Credit: smoking is the lurking (confounding) variable

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