1. A 2014 study by the reputable Gallup organization estimates that 44% of U.S.
ID: 2949500 • Letter: 1
Question
1. A 2014 study by the reputable Gallup organization estimates that 44% of U.S. adults are underemployed. Underemployed means the person wants to work full time but is employed part time or unemployed. We want to know if the proportion is smaller this year. We select a random sample of 100 U.S. adults this year and find that 40% are underemployed. After carrying out the hypothesis test for p = 0.44 compared to p < 0.44, we obtain a P?value of 0.21. Which of the following interpretations of the P?value is correct?
A. There is a 21% chance that 44% of U.S. adults are underemployed this year
B. There is a 21% chance that 40% of U.S. adults are underemployed this year.
C. There is a 21% chance that 40% or fewer U.S. adults are underemployed this year if 44% were underemployed in 2014.
D. There is a 21% chance that a sample of 100 U.S. adults will have 40% or fewer underemployed if 44% of the population is underemployed this year.
2. A school district claims that the normal attendance rate for their schools is 95%. An educational advocate believes that the true figure is lower. She chooses a school day in October and chooses 120 random students from the district. On that day, 12.5% of the students missed school.
Can she conduct a hypothesis test to determine whether the proportion of students who attend school is lower than 0.95?
A. Yes, because the sample is random, so it represents the students in the district.
B. Yes, because (120)(0.125) and (120)(0.875) are both at least 10. This means the normal model is a good fit for the sampling distribution.
C. No, because even though (120)(0.95) is at least 10, (120)(0.05) is less than 10. This means the normal model is NOT a good fit for the sampling distribution.
3. A school district claims that the normal attendance rate for their schools is 95%. An educational advocate believes that the true figure is lower. She chooses a school day in October and chooses 120 random students from the district. On that day, 12.5% of the students missed school.
Can she conduct a hypothesis test to determine whether the proportion of students who attend school is lower than 0.95?
A. Yes, because the sample is random, so it represents the students in the district.
B. Yes, because (120)(0.125) and (120)(0.875) are both at least 10. This means the normal model is a good fit for the sampling distribution.
C. No, because even though (120)(0.95) is at least 10, (120)(0.05) is less than 10. This means the normal model is NOT a good fit for the sampling distribution.
4. Sample size: A researcher is trying to decide how many people to survey. Which of the following sample sizes will result in a confidence interval with the largest width?
A. 300
B. 700
C. 1000
D. The width depends on the sample proportion.
5. Texting while driving: The accident rate for students who didn’t text while using a driving simulator was 7%. In a driver distraction study of 1,876 randomly selected students, the accident rate for students who texted while driving was higher than 7%. This difference was statistically significant at the 0.05 level.
Which of the following best describes how we should interpret these results?
A. Because of the large size of the sample, these results are strong evidence that texting accounts for a much larger proportion of accidents in the population of student drivers.
B. With a large sample, statistically significant results suggest a large increase in the accident rate for the texting group over the control group.
C. With a large sample, statistically significant results may actually be only a small improvement over the control group (depending on the size of the increase in percentages).
D. Regardless of the sample size, a statistically significant result means there is a meaningful difference in the accident rates for the two groups.
6. Police body cameras: A survey of New York State residents asked about police officers having to wear video cameras on duty. The question stated, “Do you agree or disagree that police officers should carry video cameras for the purposes of filming their activities while on duty?” Most (88%) respondents agreed with this statement.
Do Californians share the same opinion? A California-based civil rights group conducted a similar survey by randomly selecting 500 California residents, and 425 agreed that police officers should carry video cameras for the purposes of filming their activities while on duty.
Conduct a hypothesis test to determine if the proportion of California residents who agree is different from New York residents. Use a 5% significance level to make your decision. Use the applet to determine the P?value.
http://www.futurity.org/police-poll-new-york-942752/
Click here to open the applet.
Which of the following is an appropriate conclusion based on the results?
A. The survey provides strong evidence that the proportion of California residents who agree that police officers should carry video cameras for the purposes of filming their activities while on duty is significantly different from the proportion of New York residents.
B. The survey suggests that the proportion of California residents who agree that police officers should carry video cameras for the purposes of filming their activities while on duty is 85%.
C. Of the California residents surveyed, 85% agree that police officers should carry video cameras for the purposes of filming their activities while on duty, but this is not strong enough evidence to conclude that the proportion of California residents who agree is significantly different from the proportion of New York residents.
D. This survey suggests that 88% of California residents surveyed agree that police officers should carry video cameras for the purposes of filming their activities while on duty.
7. Gender and College Students: According to the U.S. Department of Education, approximately 57% of students attending colleges in the U.S. are female. A statistics student is curious whether this is true at her college. She tests the hypotheses H0: p = 0.57 versus Ha: p ? 0.57.
She plans to use a significance level of 0.05. She calculates her test statistic to be 1.42. Using the applet, which is the P?value? Click here to open the applet.
A. P?value = 0.078
B. P?value = 0.156
C. P?value = 0.922
D. P?value = 0.05
Explanation / Answer
(1)
There is a 21% chance that 40% or fewer U.S. adults are underemployed this year if 44% were underemployed in 2014.
This is the case of a left tailed test, hence this is the correct interpretation.
(2)
B. Yes, because (120)(0.125) and (120)(0.875) are both at least 10. This means the normal model is a good fit for the sampling distribution.
We check the condition that n*p > 10 and n*(1-p) > 10, where p is the sample proportion.
(3)
This has same answer as part (2) above.
(4)
A. 300
This is because width of confidence interval is inversely proportional to square root of sample size. So the larger the sample size the smaller is the width.
(5)
C. With a large sample, statistically significant results may actually be only a small improvement over the control group (depending on the size of the increase in percentages).
As sample size increases beyond a certain limit, every difference is significant, which shows that sample size has a strong effect on p-value.
Too many questions in one single question.
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