Problems from Intro Stats by DeVeaux, Velleman and Bock

Crossing Lake Ontario Between 1954 and 2003, swimmers have crossed Lake Ontario 43 times. Both women and men have made the crossing. A summary of the data regarding their times is as follows.

Group / Count / Mean (min) / Standard Deviation (min)
female / 22 / 1271.59 / 261.111
male / 20 / 1196.75 / 304.369

What is the difference between average crossing times for female and male swimmers (out of all swimmers in the world) to cross the lake?

Yogurt Is there a difference in calories between servings of strawberry and vanilla yogurt? How much?

Brand / Strawberry (cal) / Vanilla (cal)
America’s Choice / 210 / 200
Breyer’s Lowfat / 220 / 220
Columbo / 220 / 180
Dannon Light ‘n’ Fit / 120 / 120
Dannon Lowfat / 210 / 230
Dannon LaCreme / 140 / 140
Great Value / 180 / 80
La Yogurt / 170 / 160
Mountain High / 200 / 170
Stonyfield Farm / 100 / 120
Yoplait Custard / 190 / 190
Yoplait Light / 100 / 100

Normal temperature A researcher measured the body temperatures of a randomly selected group of adults. The data he collected are summarized below.

a)Find a 98% confidence interval for the mean body temperature among all adults in the world.

b)98.6°F is commonly assumed to be “normal.” Do these data suggest otherwise? Explain.

Count / 50
Mean / 98.285°F
Median / 98.200°F
Standard deviation / 0.6824°F
Interquartile range / 1.050°F

Cuckoo eggs Cuckoos lay their eggs in the nests of other (host) birds. The eggs are then adopted and hatched by the host birds. But the potential host birds lay eggs of different sizes. Does the cuckoo use different length eggs for different foster species? Test this for two different species, using the data below to conduct a hypothesis test and compute a 95% confidence interval for the difference in mean egg length in the two species.

Egg length for Sparrow (mm) / Egg length for Robin (mm) / Egg length for Wagtail (mm)
20.85 / 21.05 / 21.05
21.65 / 21.85 / 21.85
22.05 / 22.05 / 21.85
22.85 / 22.05 / 21.85
23.05 / 22.05 / 22.05
23.05 / 22.25 / 22.45
23.05 / 22.45 / 22.65
23.05 / 22.45 / 23.05
23.45 / 22.65 / 23.05
23.85 / 23.05 / 23.45
23.85 / 23.05 / 24.05
24.05 / 23.05 / 24.05
25.05 / 23.05 / 24.05
23.25 / 24.85
23.85

Doritos Some students checked 6 bags of Doritos marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the masses (in grams): 29.2, 28.5, 28.7, 28.9, 29.1, 29.5.

a)Test the company’s claim about the net weight.

b)Compute a 95% confidence interval for the mean net weight of such bags of these chips.

Job satisfaction A company institutes an exercise break for its workers to see if this will improve job satisfaction, as measured by a questionnaire. Scores for 10 randomly selected workers, each one measured before and after the implementation of the program, are shown.

a)Find a 95% confidence interval for the mean of the differences in scores (after minus before).

b)On average, is there a difference from before to after the implementation of the program?

Worker number / Before (unitless) / After (unitless)
1 / 34 / 33
2 / 28 / 36
3 / 29 / 50
4 / 45 / 41
5 / 26 / 37
6 / 27 / 41
7 / 24 / 39
8 / 15 / 21
9 / 15 / 20
10 / 27 / 37