Download Problems from Intro Stats by DeVeaux, Velleman and Bock Crossing

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
Egg length for Robin
Egg length for Wagtail
(mm)
(mm)
(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