S501.3 HW2 Solutions

1. a) All packages of ground beef coming from the same supplier. (Other answers are possible here.)

b) variable: weight of package (in lbs.), type: quantitative, continuous

c) sample (based on the answer in part (a))

d) sample mean (xbar) = 1.0522, sample variance (s**2) = .0275, sample S.D. s = .1657, median = 1.06

e) statistics: the values are computed from the data in the sample

2. a) Population: all 50’x50’ squares in the given tract of timber.

b) number of trees of diameter > 12" in a 50’x50’ square; quantitative, discrete. Others: average height of trees in a 50’x50’ square (quant., cont.), dominant type of tree in the square (qual., nominal), max. height in the square, many others possible.

c) sample

d) mean = 7.729, var. = 3.94, s = 1.985, median =8

e) statistics: the values are computed from the data in the sample

3. a) Population: all striped dolphins (or: all male striped dolphins). The way the question is worded, all dolphins seems to be the population of interest.

b) mercury concentration (mcgm/gm ) in the liver (quant., cont.). Others: weight of dolphin, length, age, health category

c) sample

d) mean = 236.7, median = 246.5, var. = 20,022.25, s = 141.5.

e) statistics

f) Yes: one plausible explanation is that younger dolphins would have less time in which to accumulate mercury in their bodies.

4. a) Two populations: Pop. 1 - all miniboxes of generic brand raisins; Pop. 2 - all miniboxes of Sunmaid raisins.

b) # raisins per box; quant., discrete

c) sample (actually: two samples)

d) mean (gen) = 26.214, mean (Sun) = 26.143

median (gen) = 26, median (Sun) = 26

s(gen) = 1.251, s(Sun) = 2.413

e) Based on these data, the average count is slightly higher for Generic, the medians are the same, and the variability is slightly higher for Sunmaid. Thus there is some evidence that the counts in Generic are more consistently closer to the mean. On this basis, I would choose Generic. But: what about price? (Probably higher for Sunmaid.) Quality? (Also probably higher for Sunmaid.) Size of raisins? Etc. Before making a decision, I would ask about these (and perhaps other) matters.