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AP Statistics
AP Review – Inference with Proportions
1) If a 95%confidence interval for p is (.6, .72), what conclusion can we
draw if we test H0: p= .75 vs. Ha: p ≠ .75 at  = 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: p = .30, Ha: p < .30, if you conclude that the proportion 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 proportion of council members who are in favor of a new ordinance is
(.45, .53). What does the phrase 97% confidence mean?
a) 97% of the ordinances are between .45 and .53
b) 97% of the time the proportion of council members in favor are
between .45 and .53
c) There is a 97% probability that the proportion of council
members in favor are between .45 and .53
d) There is a 97% chance that the proportion of council members in
favor are between .45 and .53
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  = .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 less than 3% of its bulbs are
defective. 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
where 15% are catfish provides evidence that the hypothesized
proportion (p0 = .12) of catfish in a lake 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
proportion of .12.
b) the sample result causes an error in the expected result.
c) a sample size of 100 would have a proportion of .15 or higher
when the true proportion is .12.
d) a sample of size 100 would provide more accurate proportion
then the hypothesized proportion.
e) None of these are correct.
8) A sample of 100 engineers in a large consulting firm indicated that
they spend 10% of their income on food. Three interns independently
calculated different confidence intervals of the true proportion of
income spent on food for all engineers in the company. The confidence
intervals were A: (.04, .16); B: (.06, .16); C: (.02, .18). 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  = 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) A hypothesis test on a null hypothesis of p0 =.5 is conducted at the
5% level of significance. The value of  is calculated and found to be
0.12 for the alternative hypothesis of pa = .57. Which of the following
statements about  is false?
a)  is the probability of failing to reject H0 when H0 is false.
b) The power of the test is 0.88.
c)  is the probability of a Type II error.
d)  is the complement of the probability of a Type I error.
e)  would decrease for an alternative hypothesis pa = .59
12) In a random survey of 450 adults, 28 % said that they felt that their
credit card dept is too high. With what degree of confidence can the
pollster say that .28 ± .04 of adults believe that their credit card debt
is too high?
a) 70.0 %
b) 91.0%
c) 94.1%
d) 95.0%
e) 96.0%
13) What is the probability of a Type II error when a hypothesis test is
being conducted at the 5% significance level ( = .05)?
a) .05
b) .10
c) .90
d) .95
e) There is insufficient information to answer this question.
14) When leaving for school on an overcast morning, you make a judgment
on the null hypothesis: the weather will remain dry. What would the
results be of Type I and Type II errors?
a) Type I error: get drenched. Type II error: needlessly carry an
umbrella
b) Type I error: needlessly carry an umbrella. Type II error: get
drenched
c) Type I error: carry an umbrella & it rains. Type II error: carry
no umbrella, but weather remains dry
d) Type I error: get drenched. Type II error: carry no umbrella,
but weather remains dry
e) Type I error: get drenched. Type II error: carry an umbrella,
and it rains