Statistics and Probability for Business Management 1100
Solutions to Midterm 1

1.  
   1. (ii) number of siblings is discrete quantitative
   2. (i) favorite color is qualitative
2. Her class of 70 Business Statistics students constitute the sample; all Pitt students constitute the population
3.  
   1. 2 would be the only reasonable mean; the others are too low or too high
   2. 1.5 is the only reasonable standard deviation; .2 is already too small, and 5.5 is too large (sketch roughly what a histogram would look like)
   3. shape would be skewed right because of a few students with relatively many siblings; on the left side, it can't go any lower than zero
4.  
   1. Five Number Summary values are 1st (16), 7th (25), average of 13th and 14th (26), 20th (29), and 26th (33)
   2. Q1+1.5(IR)=29+1.5(4)=35; no values are larger than this, so there are no high outliers
   3. Omitting 16 would increase the mean (not averaging in that small value) and decrease the standard deviation (omitting outlier reduces spread)
5.  
   1. (ii) boxplot for IQs of private school students would have a higher center because there'd be fewer IQs at the low end
   2. (i) public school IQ boxplot would have more spread, taking into account some students with very low IQs
   3. (ii) both shapes should be reasonably symmetric, no reason to expect otherwise
6.  
   1. .9909
   2. 1.28
7.  
   1. mean plus or minus 2 standard deviations produces the interval from 20.6 to 25
   2. z=(24-22.8)/1.1 = 1.09; the proportion less than 1.09 is .8821, so the proportion greater is .1379, or about 14 percent
   3. smallest 3 percent correspond to z=-1.88, so x=22.8-1.88(1.1)=20.732
8.  
   1. (iii) positive because people with higher incomes would buy more expensive homes
   2. (iii) strong because r is close to 1
   3. 24+2.5(50)=149
   4. 151-149=2 thousand dollars
   5. (i) r should decrease because the cluster would be looser
   6. (iii) 100 is outside the range of income values used to produce the regression line
   7. b=2.5
9.  
   1. females:180/200 is higher than 480/600
   2. females: 100/300 is higher than 10/100
   3. (ii) rate of admission is higher for business school, and percentage of males applying is higher; note that males have a higher percentage of admissions in the combined table (490/700 higher than 280/500) so we have an example of Simpson's Paradox
10. (iii) non-response is the worst problem for mailed-out questionaires like this
11. (a) structured (although I realized that I forgot to include zero as a possiblity, so I accepted (d) one-sided)
12. (a) matched pairs
13.  
    1. 10 in the overlap, 30 remaining in C but not G, 20 remaining in G but not C, 40 outside the circles
    2. First column 10 then 20, second column 30 then 40
    3. 20/100=.2
    4. 60/100=.6
14.  
    1. P(E)=P((W and E) or (not W and E))=.85(.95)+.15(.92)=.8075+.1380=.9455
    2. .8075/.9455=.8540

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