Question

# 1. When constructing a confidence interval to estimate a population proportion, what affects the size of...

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.

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.

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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