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AP Statistics
#18 AP Review – Inference with Means
1) If a 95%confidence interval for μ is (6, 9), what conclusion can we
draw if we test H0: μ = 10 vs. Ha: μ ≠ 10 at α = 0.05?
a) reject H0
d) accept Ha
b) fail to reject H0
e) There is insufficient
c) accept H0
information given to answer.
2) Given H0: μ = 30, Ha: μ < 30, if you conclude that the mean is less
than 30 when it is actually 27, then
a) you have made a Type I error
b) you have made a Type II error
c) the result of you test was not significant
d) you have drawn a correct conclusion
e) you failed to reject the null hypothesis
3) The local news station reported that the 97% confidence interval for
the mean salary of council members is ($38,945, $41,245). What does
the phrase 97% confidence mean?
a) 97% of the salaries are between $38,945 and $41,245
b) 97% of the time the salaries are between $38,945 and $41,245
c) There is a 97% probability that the salaries are between
$38,945 and $41,245
d) There is a 97% chance that the salaries of council members
from other cities are between $38,945 and $41,245.
e) None of these are true.
4) By what factor (approximately) would the margin of error increase
if we increase the confidence level from 95% to 98%?
a) 0.43
d) 1.68
b) 0.98
e) 2.33
c) 1.19
5) A one-tailed hypothesis test is conducted at the α = .05 level of
significance resulting in a p-value = 0.032. Which of the following
conclusion is not valid?
a) A two-tailed hypothesis test for the same situation would
indicate a non-significant result.
b) The probability of making a correct decision is 0.032.
c) If the sample and population values stayed the same and the
sample size increased, then the p-value would decrease.
d) The 95% confidence interval of the sample result would
contain the expected population value.
e) All of these are valid conclusions.
6) Light bulb manufacturer claims that its bulbs have a mean life of
139.5 hours. A consumer group decides to test this hypothesis at the
5% level of significance. Which of the following is not an appropriate
interpretation of the 5% level of significance?
a) 5% is the probability of a Type I error
b) 5% is the probability of rejecting the null hypothesis when it’s
true
c) 5% is the probability of accepting the null hypothesis when it’s
false
d) 5% is the criteria for judging whether the sample statistic is
sufficiently extreme to cast doubt on the manufacturer’s claim
e) None of these is an appropriate interpretation
7) A test is conducted to determine if a random sample of 100 fish
whose mean length is 53 cm provides evidence that the hypothesized
mean length of 50.5 cm is too low. The p-value of the appropriate test
is 0.042. This p-value represents the probability that
a) the corresponding confidence interval captures the
hypothesized mean of 50.5.
b) the sample result causes an error in the expected result.
c) a sample size of 100 would have a mean of 53 cm or higher
when the true mean is 50.5 cm.
d) a sample of size 100 would provide more accurate mean then
the hypothesized mean.
e) None of these are correct.
8) A sample of 100 engineers in a large consulting firm indicated that
the mean amount of time they spend reading of pleasure each week is
1.4 hours. Three interns independently calculated different confidence
intervals of the true mean amount of time for all engineers in the
company. The confidence intervals were A: (.17, 2.63); B: (.554,
2.446); C: (1.167, 1.633). Which conclusion is valid?
a) All are calculated correctly with different levels of confidence.
b) A and C have reasonable intervals but B does not.
c) A and B have reasonable intervals but C does not.
d) B and C have reasonable intervals but A does not.
e) None of these intervals are reasonable.
9) Which of the following best describe a Type I error for a hypothesis
test?
a) It is the probability of accepting H0 when H0 is false.
b) It is the probability of rejecting H0 when H0 is true.
c) It is the complement of the power of the test.
d) It is the complement of a Type II error.
e) None of these describes a Type I error.
10) A two-tailed hypothesis test at the α = 0.05 level has a p-value of
0.072. Which of the following conclusions is valid?
a) The null hypothesis should be accepted.
b) The null hypothesis should be rejected.
c) A one-tailed test of the null hypothesis using the same sample
will be significant.
d) The p-value of 0.072 indicates the probability that the null
hypothesis is false.
e) None of these are valid conclusions.
11) The decision between a z-test for a population mean or a t-test for
a population mean is based on
a) the sample size
b) whether the samples are SRS’s or not
c) the shape of the distribution from which the samples are taken
d) the size of the standard deviation of the sample
e) None of the above.
12) A hypothesis test on a null hypothesis of μ0 = 50.5 is conducted at
the 5% level of significance. The value of β is calculated and found to
be 0.12 for the alternative hypothesis of μa = 52.25. Which of the
following statements about β is false?
a) β is the probability of failing to reject H0 when H0 is false.
b) The power of the test is 0.88.
c) β is the probability of a Type II error.
d) β is the complement of the probability of a Type I error.
e) β would decrease for an alternative hypothesis μa = 53.5
13) Which of the following statements is the reason that the Central
Limit Theorem is very important in statistics?
a) It applies for any sample size as long as the population is
normal.
b) It applies for any population distribution as long as the
population mean is known.
c) It applies for any population distribution as long as the sample
size is large.
d) It applies for any sample as long as the population distribution
is known.
e) All these statements are true.
14) The test statistic from a two-tailed hypothesis test of the mean of
the differences of pre- and post-tests of arithmetic for a class of 3rd
graders produces a p-value of 0.12. Suppose that the level of
significance is 0.02. Which of the following statements is false?
a) The p-value is the probability of a sample yielding this
difference or a larger difference when the null is true.
b) The 98% confidence interval of the true mean difference with
the same sample information includes the value of 0.
c) A one-tailed test with the same sample information will
generate a p-value of 0.06.
d) The 90% confidence interval of the true mean difference with
the same sample information includes the value of 0.
e) All of these are true statements.
Answers: 1-A, 2-D, 3-B, 4-C, 5-B, 6-C, 7-E, 8-A, 9-B, 10-E, 11-E,
12-D, 13-C, 14-A