Basic Applied Statistics 200
Solutions to Midterm 2 Fall 2002

1.  
   1. NO HIGHER THAN 2 means 0, 1, or 2: add the probabilities to get .10+.10+.25=.45
   2. (i) Sketch a quick histogram with bars of height .1, .1, .25,.3, and .25 to see that the distribution is skewed left (has a long left tail)
2.  
   1. distribution of sample mean has mean equal to population mean (210), standard deviation equal to population standard deviation divided by square root of sample size (25/9=3.57) and shape approximately normal because (ii) the population is normal, according to the problem statement
   2. P(X-bar>220)=P(Z>(220-210)/3.57)=P(Z>2.8)=P(Z<-2.8)=.0026
3.  
   1. (iii) 2 categorical variables: age here is treated as categorical, not quantitative
   2. P(G)=660/6000=.11
   3. P(G|Y)=210/1500=.14
   4. (i) more likely, since the answer to (b) is larger than the answer to (a)
4.  
   1. (i) .56 is a parameter because it describes the population (all American adults; .61 describes the sample).
   2. mean is np=1600(.56)=896, standard deviation is square root of np(1-p), or square root of 1600(.56)(.44) =19.86
   3. P(X>976)=P(Z>(976-896)/19.86)=P(Z>4.03)=0, approximately
   4. (ii) some were not telling the truth; the discrepancy can't be attributed to chance variation
5. (iii) both a high level of confidence and a narrow interval are desirable
6.  
   1. (x) 95% of 100 = 95
   2. (i) .05 of 100 = 5
7.  
   1. 5.15 plus or minus 1.96(1.69)/square root of 4356= (5.1,5.2)
   2. YES, we anticipate the test to reject Ho:mu=5.0, because 5.0 is NOT in the above interval.
   3. (iv) is the only correct choice
   4. (ii) Yes, because the sample size is large: 4356 is huge enough to render sample mean normal for any population shape.
   5. (iv) skewed right; occasionally students take much more time to graduate.
8.  
   1. Ha: mu > 0
   2. For 16-1=15 df, 3.43 is between two critical values that have p between .0025 and .001
   3. (ii) The P-value is very small, providing very strong evidence against Ho.
   4. If 2.1 had been sigma instead of s, we would have had a z distribution instead of t, and could look up the probability in Table A: .0003
9. (a) is matched pairs; two height values recorded for each individual
10.  
    1. (ii) NO, not at all; a p-value of .46 isn't even close to being small.
    2. circle the p-value of .46
    3. one-sided P-value is half the two-sided P-value: 1/2(.46)=.23
11.  
    1. (ii) fail to reject Ho even when it is false (small n leads to small test statistic which leads to large p-value)
    2. (i) find a statistically significant difference (large n leads to large test statistic which leads to small p-value)

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