Basic Applied Statistics 200 Solutions to Midterm 1 Spring 2002

1.
1. (i) Method 1 because the values tend to be lower
2. (ii) Method 2 because the stemplot has more spread
3. (i) Method 1 looks perfectly symmetric
4. (iv) neither has values far from the rest
5. (ii) mean and standard deviation because it is symmetric
6. 13, 19 (3rd value), 24, 28 (8th value), 31
7. (i) Method 1 (ranges from 11 to 27, not 13 to 31)
2.
1. 0 is the mean of a standard normal distribution
2. 1 is the standard deviation of standard normal z
3. .1003 are GREATER (.8997 would be less)
4. practically no observations are this high
5. .9772-.8413=.1359
6. look up .0404; the closest z is -1.75
7. look up .9900 (because you want the HIGHEST 1%); the closest z is 2.33
3.
1. 95% are within 2 s.d.s of the mean: 5.3 plus or minus 2(.2) goes from 4.9 to 5.7
2. z=(4.8-5.3)/.2=-2.5; the proportion below is .0062
3. no, not likely because the probability .0062 is so small
4. for .25 below, z=-.67, so x=5.3-.67(.2)=5.166
4.
1. men who died (3160/2223) have the highest proportion
2. 332/706=.47
3. 332/1692=.20
4. 374/531=.704
5.
1. tip
2. (i) increase (points slope up)
3. (iii) rather strong (points are fairly tightly clustered)
4. (v) +.83 because the relationship is fairly strong, but you could take the square root of R-Sq=.686 to be sure
5. (ii) same; r is independent of assignment of explanatory/response
6. -.35+.15(63.30)=9.19
7. 12-9.19=2.81
8. (iii) it predicts 15% of the bill minus 35 cents (see regression equation)
9. (i) random scatter is a good thing in the residual plot
10. (ii) decrease because it would make the clustering looser
6.
1. (iii) not enough replication; 5 each are small groups
2. (i) no comparison is made
3. (ii) no randomization; people chose what medication to take
7.
1. 25 is the number actually examined
2. observational study; the pediatrician does not manipulate any variables, she only observes