Multiple Choice Identify the
choice that best completes the statement or answers the question.
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1.
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In an opinion poll, 25% of a random sample of 200
people said that they were strongly opposed to having a state lottery. The standard error of
the sample proportion is approximately
a. | 0.03 | b. | 0.25 | c. | 0.0094 | d. | 6.12 | e. | 0.06 |
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2.
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You want to design a study to estimate the
proportion of students on your campus who agree with the statement, “The student government is
an effective organization for expressing the needs of students to the administration.”
You will use a 95% confidence interval and you would like the margin of error to be 0.05 or
less. The minimum sample size required is approximately
a. | 22 | b. | 1795 | c. | 385 | d. | 271 | e. | None of the
above. |
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3.
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An opinion poll asks a random sample of adults
whether they favor banning ownership of handguns by private citizens. A commentator believes
that more than half of all adults favor such a ban. The null and alternative hypotheses you
would use to test this claim are:
a. |  |
b. |  |
c. |  |
d. |  |
e. | None of the
above. |
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4.
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An SRS of size 100 is taken from a population
having proportion 0.8 successes. An independent SRS of size 400 is taken from a population
having proportion 0.5 successes. The sampling distribution of the difference in sample
proportions has what mean?
a. | 0.3 | b. | 0.15 | c. | The smaller of 0.8
and 0.5 | d. | The mean cannot be determined without the sampling
results. | e. | None of the
above. |
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5.
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The college newspaper of a large Midwestern
university periodically conducts a survey of students on campus to determine the attitude on campus
concerning issues of interest. Pictures of the students interviewed along with quotes of their
responses are printed in the paper. Students are interviewed by a reporter
“roaming” the campus selecting students to interview “haphazardly.” On a
particular day the reporter interviews five students and asks them if they feel there is adequate
student parking on campus. Four of the students say no.
Which of the following conditions for
inference about a proportion using a confidence interval are violated in this example?
a. | The data are an SRS from the population of
interest. | b. | The population is at least ten times as large as the
sample. | c. | 10 and . |
d. | We are interested
in inference about a proportion. | e. | More than one
condition is violated. |
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6.
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A 95% confidence interval for p, the
proportion of Canadian beer drinkers who prefer Lion Red was found to be (0.236,0.282). Which
of the following is correct?
a. | About 95% of beer drinkers have between a 23.6% and a
28.2% chance of drinking Lion Red. | b. | There is a 95%
probability that the sample proportion lies between 0.236 and 0.282. | c. | If a second sample was taken, there is a 95% chance that its confidence
interval would contain 0.25. | d. | This confidence
interval indicates that we would likely reject the hypothesis H0: p =
0.25. | e. | We are reasonably certain that the true proportion of
beer drinkers who prefer Lion Red is between 24% and 28%. |
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7.
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In a large Midwestern university (the class of
entering freshmen being on the order of 6000 or more students), an SRS of 100 entering freshmen in
1993 found that 20 finished in the bottom third of their high school class. Admission standards
at the university were tightened in 1995. In 1997 an SRS of 100 entering freshmen found that 10
finished in the bottom third of their high school class. Let p1 and
p2 be the proportion of all entering freshmen in 1993 and 1997, respectively, who
graduated in the bottom third of their high school class.
What conclusion should we
draw?
a. | We are 95% confident that the admissions standards have
been tightened. | b. | Reject
H0 at the = 0.01 significance level. |
c. | Fail to reject H0 at the = 0.05 significance
level. |
d. | There is significant evidence of a decrease in the
proportion of freshmen who graduated in the bottom third of their high school class that were
admitted by the university. | e. | If we reject
H0 at the = .05 significance level based on these results, we
have a 5% chance of being wrong. |
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8.
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A radio talk show host with a large audience is
interested in the proportion p of adults in his listening area think the drinking age should
be lowered to eighteen. To find this out, he poses the following question to his
listeners. “Do you think that the drinking age should be reduced to eighteen in light of
the fact that eighteen-year-olds are eligible for military service?” He asks listeners to
phone in and vote “yes” if they agree the drinking age should be lowered and
“no” if not. You are told that the proportion of those who phoned in
and answered “yes” is = 0.70, and the standard error SE of
the proportion is 0.0459. The number of people who phoned in
a. | is 50. | b. | is 99. | c. | is
100. | d. | is 200. | e. | cannot be determined from the information
given. |
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9.
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In a poll, (a) some people refused to answer
questions, (b) people without telephones could not be in the sample, and (c) some people never
answered the phone in several calls. Which of these sources is included in the ±2% margin
of error announced for the poll?
a. | Only source (a). | b. | Only source (b). | c. | Only source
(c). | d. | All three sources of error. | e. | None of these sources of error. |
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10.
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A polling organization announces that the
proportion of American voters who favor congressional term limits is 64 %, with a 95% confidence
margin of error of 3%. If the opinion poll had announced the margin of error for 80% confidence
rather than 95% confidence, this margin of error would be
a. | 3%, because the same sample is
used. | b. | Less than 3%, because we require less
confidence. | c. | Less than 3%,
because the sample size is smaller. | d. | Greater than 3%,
because we require less confidence. | e. | Greater than 3%,
because the sample size is smaller. |
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