Download Multiple Choice - Troy City Schools

AP Stats
Test 4
Disclaimer: You have one class period to complete this test. You may write on this
test; in fact, put your NAME on the test. The 15 multiple-choice questions are worth a
total of 75 points. The extended response is worth 25 points.
Multiple Choice
1. A poll was conducted in the San Francisco Bay Area after the San Francisco
Giants lost the World Series to the Anaheim Angles about whether the team
should get rid of a pitcher who lost two games during the series. Five hundred
twenty-five adults were interviewed by telephone, and 55% of those responding
indicated that the Giants should get rid of the pitcher. It was reported that the
survey had a margin of error of 3.5%. Which of the following best describes what
is meant by a 3.5% margin or error?
a. About 3.5% of the respondents were not Giants fans, and their opinions
had to be discarded.
b. It’s likely that the true percentage that favor getting rid of the pitcher is
between 51.5% and 58.5%.
c. About 3.5% of those contacted refused to answer the question.
d. About 3.5% of those contacted said they had no opinion on the matter.
e. About 3.5% thought their answer was in error and are likely to change
their mind.
2. A hypothesis test was used to test H0: μ = 0.3 vs. HA: μ ≠ 0.3. The finding was
significant for α = 0.05 but not for α = 0.04. A two-sided confidence interval for
μ is constructed. Which of the following is the smallest confidence level for
which the confidence interval will not contain 0.3?
a.
b.
c.
d.
e.
90%
92%
95%
99%
96%
3. Two sampling distributions of a sample mean from the same population are to be
constructed. The first (I) has sample size n1 = 8 and the second (II) has sample
size n2 = 35. Which of the following statements is not true?
a. Both sampling distributions I and II will have the same mean.
b. Distribution I is more variable than Distribution II.
c. The shape of Distribution I will be similar to the shape of the population
from which it was drawn.
d. The shape of each sampling distribution will be approximately normal.
e. The shape of Distribution II will be approximately normal.
4. Which of the following is the best reason to use a t-distribution rather than a
normal distribution when testing for a population mean?
a.
b.
c.
d.
e.
You should always use a t-distribution for small samples.
You are unable to compute the sample standard deviation.
The normal distribution is too variable.
The population standard deviation is unknown.
t-distributions are very similar to the normal distribution for large samples.
5. A national polling organization wishes to generate a 98% confidence interval for
the proportion of voters who will vote for a candidate in the next election. The
poll is to have a margin of error of no more than 3%. What is the minimum
sample size needed for this interval?
a.
b.
c.
d.
e.
6032
1508
39
6033
1509
6. A survey is conducted to determine the percentage of students at state universities
that change their major at least once. In a SRS of 100 students, 78% indicated
that they graduated with a major different from the one with which they entered
college. Which of the following is the proper meaning of a 95% confidence level
estimate for the percentage of students who change their major?
a. We are 95% certain that 78% of student change their major.
b. Between 69.9% and 86.1% of student change their majors 95% of the
time.
c. 95% of the students change their majors between 69.9% and 96.1% of the
time.
d. In repeated samplings of 100 students, there is a 95% chance that the
proportion of students who change their major in any given sample is
between 69.9% and 86.1%.
e. In repeated samplings of 100 students, 95% of the resulting intervals will
contain the true proportion of students who change their major.
7. In general, how does tripling the sample size change the confidence interval size?
a.
b.
c.
d.
e.
It triples the interval size.
It divides the interval size by 3.
It multiplies the interval size by 1.732.
It divides the interval size by 1.732.
This question cannot be answered without knowing the sample size.
8. The sampling distribution of the sample mean is close to the normal distribution
a. Only if both the original population has a normal distribution and n is
large.
b. If the standard deviation of the original population is known.
c. If n is large, no matter what the distribution of the original population.
d. No matter what the value of n or what the distribution of the original
population.
e. Only if the original population is not badly skewed and does not have
outliers.
9. Which of the following are true statements?
I.
II.
III.
a.
b.
c.
d.
e.
A study results in a 99% confidence interval estimate of (34.2,
67.3). This means that in about 99% of all samples selected by this
method, the sample means will fall between 34.2 and 67.3.
A high confidence level may be obtained no matter what the
sample size.
The central limit theorem is most useful when drawing samples
from normally distributed populations.
I only
II only
III only
I and II
I and III
10. The weight of an aspirin tablet is 300 milligrams according to the bottle label. An
FDA investigator weighs a simple random sample of 7 tables, obtains weights of
299, 300, 305, 302, 299, 301, and 303, and runs a hypothesis test of the
manufacturer’s claim. Which of the following gives the p-value of this test?
a.
b.
c.
d.
e.
P(t > 1.54) with df = 6
2P(t > 1.54) with df = 6
P(t > 1.54) with df = 7
2P(t > 1.54) with df = 7
0.5P(t > 1.54) with df = 7
11. Based on a survey of a random sample of 900 adults in the United States, a
journalist reports that 60% of adults in the United States are in favor of increasing
the minimum hourly wage. If the reported percentage has a margin of error of 2.7
percentage points, which of the following is closest to the level of confidence?
a.
b.
c.
d.
e.
80.0%
90.0%
95.0%
95.5%
99.0%
12. There were 5,317 previously owned homes sold in a western city in the year 2000.
The distribution of the sales prices of these homes was strongly right-skewed,
with a mean of $206,274 and a standard deviation of $37,881. If all possible
simple random samples of size 100 are drawn from this population and the mean
is computed for each of these samples, which of the following describes the
sampling distribution of the sample mean?
a. Approximately normal with mean $206,274 and standard deviation $3,788
b. Approximately normal with mean $206,274 and standard deviation
$37,881
c. Approximately normal with mean $206,274 and standard deviation $520
d. Strongly right-skewed with mean $206,274 and standard deviation $3,788
e. Strongly right-skewed with mean $206,274 and standard deviation
$37,881
13. In a random sample of 17 ACT scores from the class of 2007, the mean was 21.29
and the standard deviation was 3.42. Assume the conditions for inference are
met. What are the correct conclusions based upon the given hypotheses?
a. If H0: μ0 = 23 and Ha: μ < 23, reject at the α level of 0.05 because the pvalue is larger than 0.05.
b. If H0: μ0 = 23 and Ha: μ > 23, reject at the α level of 0.05 because the pvalue is larger than 0.05.
c. If H0: μ0 = 23 and Ha: μ ≠ 23, reject at the α level of 0.05 because the pvalue is less than 0.05.
d. If H0: μ0 = 23 and Ha: μ ≠ 23, fail to reject at the α level of 0.05 because
the p-value is larger than 0.05.
e. If H0: μ0 = 23 and Ha: μ ≠ 23, reject at the α level of 0.05 because the pvalue is smaller than 0.05.
14. A recent study was conducted to investigate the duration of time required to
complete a certain manual dexterity task. The reported mean was 10.2 seconds
with a standard deviation of 16.0 seconds. Suppose the reported values are the
true mean and standard deviation for the population of subjects in the study. If a
random sample of 144 subjects is selected from the population, what is the
approximate probability that the mean of the sample will be more than 11.0
seconds?
a.
b.
c.
d.
e.
0.1151
0.2743
0.7257
0.8849
Based on the values of the true mean and true standard deviation, it can be
concluded that the population distribution is not normal and therefore the
probability cannot be calculated.
15. A large sample 98% confidence interval for the proportion of hotel reservations
that are canceled on the intended arrival day is (0.048, 0.112). What is the point
estimate for the proportion of hotel reservations that are canceled on the intended
arrival day from which this interval was constructed?
a.
b.
c.
d.
e.
0.032
0.064
0.080
0.160
It cannot be determined from the information given.
Show all your work. Indicate clearly the methods you use, because you will be scored on
the correctness of your methods as well as on the accuracy and completeness of your
results and explanations.
16. During a flu vaccine shortage in the United States, it was believe that 45 percent of
vaccine-eligible people received the flu vaccine. The results of a survey given to a
random sample of 2,350 vaccine-eligible people indicated that 978 of the 2,350 people
had received the flu vaccine.
a) Construct a 99 percent confidence interval for the proportion of vaccine-eligible
people who had received the flu vaccine. Use your confidence interval to comment on
the belief that 45 percent of the vaccine-eligible people had received the flu vaccine.
b) Suppose a similar survey will be given to vaccine-eligible people in Canada by
Canadian health officials. A 99 percent confidence interval for the proportion of people
who will have received the flu vaccine is to be constructed. What is the smallest sample
size that can be used to guarantee that the margin of error will be less than or equal to
0.02.