Question

**1. When constructing a confidence interval to estimate a
population proportion, what affects the size of the margin of
error?**

A. The sample size

B. The sample proportion

C. The confidence level

D. All of the above affect the size of the margin of error

E. None of the above affect the size of the margin of error

**2. What percentage of couples meet through online dating
apps? A survey of a random sample of couples finds that 12% say
they met through an online dating app. This means the sample
proportion would be**

A. 0.0120.

B. 0.1200.

C. 0.0012.

D. 1.2000.

E. It’s impossible to answer this question without knowing the sample size.

**3. What proportion of college students are basketball
fans? You survey a random sample of 350 college students, and you
find that 137 of these students indicate they are basketball fans.
Use this information to construct a 95% confidence interval in
order to estimate the population proportion of college students who
are basketball fans. Note: Answers may vary due to rounding. Round
your sample proportion to three decimal places as you are engaging
in calculations and try not to do a lot of other rounding until you
get to the very end of your calculations. Choose the answer below
that is closest to what you obtain.**

A. 0.286 to 0.496

B. 0.309 to 0.473

C. 0.340 to 0.442

D. 0.365 to 0.417

E. 0.388 to 0.394

**4. Refer to the previous question about college students
who are basketball fans. Which of the following statements is a
correct 95% confidence statement for the interval in the previous
question?**

A. We are 95% confident the sample proportion of college students who are basketball fans is within the computed interval.

B. We are 95% confident the population proportion of college students who are basketball fans is within the computed interval.

C. We are confident that 95% of college students in the population are basketball fans.

D. We are confident that 95% of college students in the sample are basketball fans.

E. We are 95% confident no errors were made in constructing the confidence interval.

**5. Bobby and Cindy are each attempting to estimate the
proportion of families in their neighborhood who have four or more
children. Bobby selects a random sample of 40 families and finds
the sample proportion to be 0.15. Cindy selects a different random
sample of 40 families and also finds the sample proportion to be
0.15. Bobby uses his sample proportion to construct a 99%
confidence interval, and Cindy uses her sample proportion to
construct a 90% confidence interval. Who will have the wider
confidence interval?**

A. Bobby

B. Cindy

C. Both intervals will have the same width since the sample sizes are the same.

D. Both intervals will have the same width since the sample proportions are the same.

E. Both C and D are correct.

**6. Cori has constructed a 95% confidence interval in
order to estimate the proportion of high school athletes who go on
to become college athletes. Her confidence interval ends up being
0.04 to 0.10. This means the sample proportion must be**

A. 0.03.

B. 0.06.

C. 0.07.

D. 0.14.

E. It is impossible to answer this question without more information.

**7. You want to estimate the proportion of students at
OSU who use the app TikTok. You select a random sample of 280 OSU
students and find that 51% use TikTok. If you want to construct a
90% confidence interval, what will the margin of error be? Again,
attempt to round as little as you can along the way, and choose the
answer below that is closest to what you obtain.**

A. 5.8%

B. 6.2%

C. 2.7%

D. 3.3%

E. 4.9%

**8. A Pew Research Center poll surveyed a random sample
850 voters and asked them if they support legalizing the use of
marijuana. A Gallup poll surveyed a random sample of 1200 voters,
from the same population that the Pew Research Center surveyed
from, and asked the same question about legalizing the use of
marijuana. Assume that the sample proportion who support legalizing
the use of marijuana is exactly the same for each poll. If each
poll goes on to construct a 95% confidence interval, how will the
margins of error compare for the two polls?**

A. The Pew Research Center margin of error will be the same as the Gallup margin of error.

B. The Pew Research Center margin of error will be smaller than the Gallup margin of error.

C. The Pew Research Center margin of error will be larger than the Gallup margin of error.

D. There is not enough information available here to judge how the margins of error will compare.

**9. A random sample of 450 Cincinnati residents was asked
which chili they prefer: Skyline Chili or Gold Star Chili. Suppose
that 45% of those surveyed said they prefer Skyline Chili. When a
95% confidence interval was constructed based on this data, the
interval ended up being from 40.4% to 49.6%. Based on this
information, which of the following statements is
correct?**

A. The margin of error is 45%.

B. The value of 45% is a statistic.

C. The value of 45% is a parameter.

D. It would be impossible to know what the margin of error is without more information.

E. If we were to select many more random samples of size n = 450 from the population of Cincinnati residents, 95% of the resulting confidence intervals would be from 40.4% to 49.6%.

**10. In a survey of a random sample of 1075 drivers, 36%
of the drivers admitted to talking on a cell phone while driving.
The survey reported a margin of error of ±4 percentage points, at a
99% confidence level. Which of the following best describes what is
meant by the survey having a margin of error of ±4 percentage
points?**

A. Four percent of those surveyed chose not to respond to any survey questions.

B. It would not be surprising if 4% of the population of drivers talks on a cell phone while driving.

C. Between 32% and 40% of all drivers talk on a cell phone while driving.

D. Between 344 and 430 of the 1075 drivers who were surveyed responded that they talk on a cell phone while driving.

E. The survey used a method that gets an answer within 4% of the truth about the population approximately 99% of the time.

Answer #1

1) D. All of the above affect the size of the margin of error

2) B. 0.1200.

3)

Level of Significance, α =
0.05

Number of Items of Interest, x =
137

Sample Size, n = 350

Sample Proportion , p̂ = x/n =
0.3914

z -value = Zα/2 = 1.960 [excel
formula =NORMSINV(α/2)]

Standard Error , SE = √[p̂(1-p̂)/n] =
0.02609

margin of error , E = Z*SE = 1.960
* 0.02609 = 0.0511

95% Confidence Interval is

Interval Lower Limit = p̂ - E = 0.39143
- 0.05113 = 0.34030

Interval Upper Limit = p̂ + E = 0.39143
+ 0.05113 = 0.44256

95% confidence interval is (
0.340 < p < 0.442)

**C. 0.340 to 0.442**

**4)**

B. We are 95% confident the population proportion of college students who are basketball fans is within the computed interval.

5) A. Bobby

6) sample proprotion = (0.04+0.10)/2 = 0.07

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