Transcript IE241 Problems 2

IE241 Problems 2
1. In a poll taken among college students,
46 of 200 fraternity men favored a
certain proposition, whereas 51 of 300
nonfraternity men favored it. Is there a
real difference of opinion on this
proposition?
2. A test of 200 youths and 500 adults
showed that 50 of the youths and 60 of
the adults were poor drivers. Test the
claim that the youth percentage of poor
drivers is 10 percentage points higher
than the adult percentage of poor
drivers vs the claim that the youth
percentage is more than 10 percentage
points higher than the adult percentage.
3. Two sets of 100 children each were
taught to read by two different methods.
After the instruction was over, each
class took a reading test. For group A,
the mean = 73.4 and the standard
deviation = 8. For group B, the mean =
70.3 and the standard deviation = 10.
Is there a difference between the two
teaching methods?
4. The number of individuals possessing
the four blood types should be in the
proportions: q2:p2+2pq:r2+2qr:2pr
Given the observed frequencies,
180, 360, 132, 98,
test for compatibility with p = .4,
q = .4, r = .2.
5. A new drug claims to be effective in curing
colds. In an experiment on 164 people with
colds, half were given the drug, and half, a
placebo. Is the drug effective if the results
were:
Helped
Harmed
No effect
Placebo
52
44
10
12
20
26
82
82
Total
96
22
46
164
Drug
Total
6. Given that X is normally distributed, assume
that the results of a sample of size 20 had a
mean = 42 and s = 5. (a) Test the hypothesis
that σ = 8. (b) Test the hypothesis that μ = 45.
7. Two random samples are taken from two
normal populations. Test the hypothesis that
μ1 = μ2. Make sure that your test is valid.
Sample 1 Sample 2
n
10
12
mean
20
24
s
5
6
8. The following data give the protein gains of
20 rats. Half of them received their protein
from raw peanuts and the other half, from
roasted peanuts. Test to see whether roasting
the peanuts had any effect on protein value.
Is the test valid?
Mean Variance
raw
57.9
31.21
roasted
55.8
21.07
9. The following table gives data on the
hardness of wood stored outside and inside.
Test to see if the variability of hardness is
affected by weathering.
Outside Inside
n
mean
s
40
100
117
132
14.897 16.589
10. Coated and uncoated steel pipes were
tested for corrosion effects. The results are
shown in the table below.
Pipes
n
Mean
Coated
20 44.45
Uncoated 20 51.4
Variance
88.47
104.88
Test the hypothesis that the difference
between the means = 0. Then find the 95%
confidence interval for the difference between
the means.
11. A thousand people were classified by
gender and color-blindness, with results as
shown below. Are gender and colorblindness independent?
Normal
Color-blind
Total
Male
Female
442
38
480
514
6
520
Total
956
44
1000
12. Twelve pairs of runners have been matched
with respect to ability. Each member of a pair
is given a pill before the race. One member of
each pair is given a stimulant in his pill, but the
other is not. Each runner runs a race and the
times are recorded below. Is the stimulant
effective? Compute a 95% confidence interval
for the difference between the means.
Pair
1
2
3
4
5
6
7
8
9
10
11
12
Stimulant 64 62 63 61 61 59 62
64
65
62
63
63
No Stim
66
65
64
65
63
64 63 65 62 63 61 62
13. In an industrial experiment, the time needed
to do a job by method 1 was compared with
the time needed to the same job by method 2.
Given the times shown below, is method 1
better than method 2? If so, do a 95%
confidence interval on the time difference.
Method 1 Method 2
mean
53.7
55.375
variance
15
18
n
30
40
13.