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AP Statistics
1) Changing from a 95% confidence interval estimate to a 99% confidence
interval estimate, with all other things being equal,
a) increases the interval size by 4%
b) decrease the interval size by 4%
c) increases the interval size by 31%
d) decreases the interval size by 31%
e) This question cannot be answered without knowing the sample size.
2) The 99.7% confidence interval for the mean length of frog jumps is (12.64
cm, 14.44 cm). Which of the following statements is a correct interpretation of
99.7% confidence?
a) Of the total number of frogs in your area of the country, 99.7% can
jump between 12.64 cm and 14.44 cm.
b) There’s a 99.7% chance that the mean length of frog jumps falls
between 12.64 cm and 14.44 cm.
c) If we were to repeat this sampling many times, 99.7% of the confidence
intervals we could construct would contain the true population mean.
d) 99.7% of the confidence intervals we could construct after repeated
sampling would go from 12.64 cm to 14.44 cm.
e) There’s a 99.7% chance that any particular frog I catch can jump
between 12.64 cm and 14.44 cm.
3) One month the actual unemployment rate in France was 13.4%. If during that
month you took a survey of 100 Frenchmen and constructed a confidence
interval estimate of the unemployment rate, which of the following would be
true?
I.
The center of the interval was 13.4
II.
The interval contained 13.4
III.
A 99% confidence interval contained 13.4
a) I and II
d) I, II, and III
b) I and III
e) None of the above gives the
c) II and III
complete set of true responses
4) In a test for acid rain, 49 water samples showed a mean pH level of 4.4.
(Assume σ = 0.35) Find a 90% confidence interval for the mean pH level.
a) 4.4 + 0.098
d) 4.4 + 0.35
b) 4.4 + 0.08225
e) 4.4 + 0.1027
c) 4.4 + 0.1288
AP Review - Confidence Intervals (z)
5) Two confidence intervals from the same sample are (16.4, 29.8) and (14.3,
31.9). What is the sample mean, and if one estimate is at a 95% level while the
other is at the 99% level, which is which?
a) x  23.1 : (16.4, 29.8) is the 95% level
b) x  23.1 : (16.4, 29.8) is the 99% level
c) It is impossible to completely answer this question without knowing the
sample size.
d) It is impossible to completely answer this question without knowing the
sample standard deviation.
e) It is impossible to completely answer this question without knowing both
the sample size and the standard deviation.
6) Hospital administrators wish to learn the average length of stay of all surgical
patients. A statistician determines that, for a 95% confidence level of the
average length of stay to be within + 0.5 days, 50 surgical patients’ records will
have to be examined. How many records should be looked at to obtain a 95%
confidence level to within + 0.25 days?
a) 25
d) 150
b) 50
e) 200
c) 100
7) The number of accidents per day at a large factory is noted for each of 64 days
with x  3.58 . (Assume σ = 1.52) With what degree of confidence can we assert
that the mean number of accidents per day at the factory is between 3.20 and
3.96?
a) 48%
d) 95%
b) 63%
e) 99%
c) 90%
8) Two 90% confidence intervals are obtained: I (28.5, 34.5) and II (30.3, 38.2).
If the sample sizes are the same, which interval has the larger standard
deviation? If the standard deviations are the same, which interval has the larger
sample size?
a) I, I
b) I, II
c) II, I
d) II, II
e) More information is needed to answer these questions.