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```1. For a one sample z interval for a population mean,
changing from 95% confidence to 90% confidence, with all
other things being equal,
A.
B.
C.
D.
E.
Increases the interval size by 16%
Decreases the interval size by 16%
Increases the interval size by 19%
Decreases the interval size by 19%
This question can’t be answered without knowing the
sample size.
2. In a test for the amount of caffeine in a particular brand
of coffee, an SRS of 61 samples showed a mean amount of
caffeine to be 95 mg per cup of the coffee with a standard
deviation of 5 mg per cup. Estimate the amount of
caffeine in a cup of this type of coffee (in mg) with 95%
confidence.
A.
B.
C.
D.
E.
95 ± 1.26
95 ± 1.28
95 ± 2.56
95 ± 5
95 ± 5.5
3. The number of accidents per day at a particular
intersection is recorded for a sample of 100 days. The
average was 2.1 with a standard deviation of 0.59. With
what degree of confidence can we say that the mean
number of accidents per day at this intersection is
between 2.0144 and 2.1856?
A.
B.
C.
D.
E.
80%
83%
85%
90%
92%
4. What sample size should be chosen to find the mean
number of visitors per month to a local gym to within ± 0.5
at a 98% confidence level. Assume the standard deviation
is 5.3.
A.
B.
C.
D.
E.
25
105
224
608
1231
5. In general, reducing the sample size
A.
B.
C.
D.
Increases the margin of error
Decreases the margin of error
Has no effect on the margin of error
Could increase or decrease the margin of error,
depending on the actual size of the sample
6. In general, increasing the confidence level
A.
B.
C.
D.
Increases the margin of error
Decreases the margin of error
Has no effect on the margin of error
Could increase or decrease the margin of error,
depending on the actual confidence level
7. It is believed that a new marketing technique will result in an
increase of \$1030 in sales per month. A market research firm
carries out a two-tailed test on a sample of 30 months in which the
new technique is used. The average increase in sales is \$979 with a
standard deviation of \$108. What conclusion should be made?
A. P = 0.0075. The result is significant for α = 0.01, α = 0.05, and α
= 0.1
B. P = 0.0075. The result is not significant for α = 0.01, α = 0.05, or
α = 0.1
C. P = 0.015 . The result is significant for α = 0.01, α = 0.05, and α =
0.1
D. P = 0.015 . The result is significant for α = 0.01, but not for α =
0.05, and α = 0.1
E. P = 0.015 . The result is not significant for α = 0.01, but is for α =
0.05, and α = 0.1
8. A tutoring company claims that their students score an average
score of 30.5 on the ACT. A statistician plans a test with a sample of
50 of their students. He will reject their claim if the average from
his sample is lower than 28. Assume the standard deviation is 8.1.
What is the probability that he mistakenly rejects a true claim?
A.
B.
C.
D.
E.
0.017
0.025
0.091
0.283
0.516
9. A two-sided significance test for a population mean, in a random
sample of size 30 has a t-score of 2.15. Is this significant at the 1%
level? The 5% level?
A.
B.
C.
D.
E.
Significant for 1% but not 5%
Significant for 5% but not 1%
Not significant for 1% or 5%
Significant for both 1% and 5%
Not enough information is given
10. A test is run to see if two different types of batteries have
different shelf lives. An SRS of 45 Type A batteries and an
independent SRS of 35 Type B batteries will be used. What is the
probability of mistakenly claiming that there is a difference when
there isn’t if the cutoff difference is ±2? Assume the standard
deviations for the shelf life of each type are 1.7 and 3.1 respectively.
A.
B.
C.
D.
E.
0.0008
0.0016
0.0079
0.056
0.087
11. A researcher believes that a new medicine will decrease the
time necessary for laboratory mice to finish a particular maze.
Twenty mice are given the new medicine and 25 mice are not given
the medicine. All the mice run through the maze and their times
are recorded. The ‘medicine’ mice have an average time of 45 sec
with a standard deviation of 3 sec. The control group have an
average time of 51 sec with a standard deviation of 2.3 sec. In
which of the following intervals is the p-value?
A.
B.
C.
D.
E.
Pvalue < 0.001
0.001 < Pvalue < 0.01
0.01 < Pvalue < 0.05
0.05 < Pvalue < 0.1
Pvalue > 0.1
12. An engineer wishes to determine the difference in life
expectancies for two brands of light bulbs. Suppose the standard
deviation of each brand is 2.7 hours. How large a sample of each
type of light bulb should be taken if he wishes to be 95% confident
of knowing the difference in life expectancies to within 1.5 hours?
Assume the same number of each light bulb will be used.
A.
B.
C.
D.
E.
5
10
18
25
34
```
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