Section 3.4 Solutions

 

3.66

a.      High bias, high variability

b.      Low bias, low variability (yeah!)

c.       Low bias, high variability

d.      High bias, low variability

 

 

3.69

a.      The variability will not change, since the sample sizes are all the same (assuming the population proportion of owners is about the same from state to state) – note that the population is always at least 100 times larger than the sample.

 

b.      If an SRS of 1/10 of 1% (0.001) of the state’s population is taken in each state, then the sample sizes will range from 500 to 35,000. Therefore the variability will change, since statistics from larger samples have smaller spreads.

 

 

3.75

a.      Starting at line 137 of Table B, I get the following “valid” numbers: 5, 3, 6, and 4. The exam scores for this sample are 73, 58, 65, and 72. The sample mean is 67.

 

b.      Continuing on line 137, I get the following 9 samples:

 

73, 65, 74, 62; sample mean = 68.5

80, 65, 62, 72; sample mean = 69.75

80, 62, 72, 66; sample mean = 70

58, 65, 62, 80; sample mean = 66.25

65, 82, 62, 62; sample mean = 67.75

73, 58, 66, 62; sample mean = 64.75

74, 72, 62, 73; sample mean = 70.25

62, 80, 65, 74; sample mean = 70.25

58, 62, 65, 74; sample mean = 64.75

 

The average of the 10 sample means is 67.925; this is somewhat close to the true value of 69.4.