STA 210 exam 2
A student in a statistics class is about to start her capstone survey sampling project. She has 113 Facebook friends and wants to distribute a questionnaire to 20 of them. Which of the following sampling plans would be the most like a real-world simple random sample?
Select 20 names at random from the 113 Friends and contact those 20 with the questionnaire.
In a 2012 Gallup poll, eighty-two percent of adult U.S. Catholics say birth control is morally acceptable. Results for this poll are based on telephone interviews conducted May 3-6, 2012, with a random sample of 1,024 adult Catholics, aged 18 and older, living in all 50 U.S. states and the District of Columbia. What is the corresponding 80% confidence interval for the proportion of all adult U.S. Catholics who feel birth control is morally acceptable?
0.82 plus or minus 0.02
In BN 2.29 you studied about the role of incentives and whether they mattered. Table 2.10 (shown below) recorded the results of the Early Response incentive. What two percentages would you use to evaluate the effect of "Incentive" versus "No Incentive" on Early Response?
16% and 32%
The website College Profile lists the average age of all 22,223 undergraduates at the University of Kentucky as 21. Let's suppose the variabilty of all 22,223 ages is 8.5. If you were to list all simple random samples of size 50 undergraduates and for each sample compute the mean, what would the mean of all those means be, more or less?
21
Please read the following excerpt a 2006 CNN/USA Today/Gallup poll. Suppose CNN/USA Today/Gallup had wanted to produce a 99.9% confidence interval that had a width of 0.02 (or 2%). What size sample would they have needed to take in order for this to happen?
27,060
A recent poll of 1500 college-age students found that 885 agreed with U.S. foreign policy toward Israel. What is the corresponding 95% confidence interval (choose closest answer)?
59% plus or minus 3%
The scores for all high school seniors taking the verbal section of the Scholastic Aptitude Test (SAT) in a particular year had a mean of 490 and a standard deviation of 100. The distribution of SAT scores is bell-shaped. A rather exclusive university only admits students who were among the highest 16% of the scores on this test. What minimum score would a student need on this test to be qualified for admittance to this university?
590
Suppose the distribution shown here represents the sampling distribution that results from spinning a two-color spinner 1020 times, recording the proportion of times a blue resulted in those 1020 spins, and repeating for a total of 100 sets of 1020 spins. About what percentage of the time did a sample percentage between 49.5 and 52.5 occur?
60%
A Gallup poll found that "with the presidential election less than a month away, 28% of Americans are satisfied with the way things are going in the U.S." The Gallup organization also reported that an 80% confidence interval for the true proportion of Americans who are satisfied with the way things are going in the U.S. is 25% to 31%. What would a 99.9% margin of error be for this poll?
7.71%
For our recent CPR assignments, how much do the calibrations count?
70%
The website College Profile lists the average age of all 22,223 undergraduates at the University of Kentucky as 21. Let's suppose the variabilty of all 22,223 ages is 8.5. If you were to list all simple random samples of size 50 undergraduates and for each sample compute the mean, what would the mean of all those means be, more or less?
8.5
The website College Profile lists the average age of all 22,223 undergraduates at the University of Kentucky as 21. Let's suppose the variabilty of all 22,223 ages is 8.5. If you were to list all simple random samples of size 50 undergraduates and for each sample compute the mean, what would the variance of all those means be, more or less?
8.5/50
In a 2012 Gallup poll, eighty-two percent of adult U.S. Catholics say birth control is morally acceptable. Results for this poll are based on telephone interviews conducted May 3-6, 2012, with a random sample of 1,024 adult Catholics, aged 18 and older, living in all 50 U.S. states and the District of Columbia. The next five questions refer to this context. What is the corresponding 95% confidence interval for the proportion of all adult U.S. Catholics who feel birth control is morally acceptable?
82% plus or minus 3%
Refer to the graphic below. We encountered this summary of the sampling distribution of the sample proportion in BN 2.23. Suppose n = 100. What are the chances of an SRS of this size yielding a phat that is somewhere between p - 0.1 and p + 0.1?
95 out of 100
What is a simple random sample?
A sample chosen in such a way that all samples of that same size have the same chance of being chosen.
What is a cross-sectional sample?
An attempt to match the sample characteristics exactly to those of the population.
What is a non-sampling error?
An error caused by something other than the fact that a sample was selected instead of the entire population.
Consider the following survey question: "The Mac operating system rarely gets infected by viruses and therefore Department of Education should only purchase Mac computers. Please answer Yes or No". What is one objection to this question, as asked?
Because of the "rarely gets infected by viruses" clause this question is a leading question.
A survey was conducted by Playboy, asking questions about the sex lives of 5,000 U.S. University and College students. One question asked: "Are you in a nude picture on someone's camera phone?" 34 percent said "yes". Name at least one error you'd expect this survey to suffer from even if all 15.9 million College and University students in the U.S. had answered, and not just 5,000.
Error caused by fabricated responses
Recall Harris Poll disclaimer mentioned in the video. Harris is a major polling organization that refuses to accompany their poll reports with a margin of error. What is one reason that was given for such a bold omission?
Harris recognizes that there are many sources of error that are not addressed by the MOE, so reporting it might be misleading.
In BN 2.29 you studied about the role of incentives and whether they mattered. There were three Phases of that study. What was Phase II?
In this Phase the 873 subjects who did not respond early (Phase I) were given an opportunity to respond in this second round. No incentives were offered.
What does the word "parameter" refer to in statistical science?
Number that describes the population
In the MOE Doesn't Apply video, what was the issue with the question "Have you often, sometimes, hardly ever, or never felt bad because you were unfaithful to your wife?"
Of the 85% who said they "never felt bad about it" surely a large part of those had never been unfaithful to their wives. But the way the question was asked this wasn't an option for an answer.
What kind of error does the margin of error address?
Random sampling error
In BN 2.20 we found that out of 594 people asked (students, researchers), 281 reported that the right way to interpret a 95% confidence interval of 0.1 to 0.4 was to say that "the probability that the true proportion is bigger than 0 is at least 95%." What is wrong with that interpretation?
That makes it sound like the parameter is random. It is not.
Robert Niles is a former mathematics geek turned journalist who is continually trying to educate other journalists about how to interpret statistical arguments. He recently noted "Don't overlook that fact that the margin of error is a 95 percent confidence interval, either. That means that for every 20 times you repeat this poll, statistics say that one time you'll get an answer that is completely off the wall." What does Niles mean by this statement?
That the "confidence" is in a repeated sampling sense; and to say one gets an interval that is "right" 95% of the time, is to say one will get a "wrong" one 5% of the time.
What are the two keys to having confidence in your parameter estimate?
The probabilistic nature of the sample selection, and some neat mathematics that follow from this.
What is sampling variability?
The variability seen in statistics from sample to sample
What is "response substitution?"
This is the tendency for survey respondents to present their answers in a way that allows them to express their opinions about other issues that aren't the topic of the survey
What is the goal of sampling?
To make inferences about a population from what we know about our sample.
Which of the following are examples of strategies for reducing non-sampling errors?
Use of inducements for non-responders Awareness of psychology of question order Use of technology-assisted confidential interview techniques
Recall the sampling distribution of the sample proportion (page 162 in your book). Specify an interval (range) in which 68% of all sample proportions based on samples of size n could be expected to occur.
Within (0.5)x(1/sqrt(n)) on either side of the parameter p.
Refer to the graphic below. We encountered this summary of the sampling distribution of the sample proportion in BN 2.23. Specify an interval (range) in which 68% of all sample proportions based on samples of size n could be expected to occur.
Within (0.5)x(1/sqrt(n)) on either side of the parameter p.
Suppose the distribution shown here represents the sampling distribution that results from spinning a two-color spinner 1020 times, recording the proportion of times a blue resulted in those 1020 spins, and repeating for a total of 100 sets of 1020 spins. From the plot can you get a pretty good idea of how likely the spinner is to land on a particular one of the two colors?
Yes. We know that the sampling distribution will peak above the parameter, which in this case seems to be about 50%. So it must be that the spinner lands on blue about 50% of the time.
The University of Kentucky has 21,441 undergraduates, with a gender distribution of 49 percent male students and 51 percent female students. You take a simple random sample of 100 undergraduates (30 males and 70 females) and ask the question "Have you ever attended a date party?" 100% of the males say "yes" and 50% of the females say "yes." If the estimate of all undergraduates who would say "yes" to this question is reweighted to reflect the distribution of males and females in the U.K. population, what would that be in this case?
about 75%
A Ph.D. candidate in the College of Education once defended her misleading and confusing questionnaire by arguing that her margin of error was low, only about 3%. This argument is:
confused, because the margin of error has nothing to do with biased questionnaire designs
Which of the following sources of error is addressed by the margin of error?
errors that comes from choosing a sample and not the entire population
What happens to the margin of error as the sample size gets larger?
it decreases
What can one say about the sampling distribution of a sample statistic based on a simple random sample?
it is about bell-shaped and peaks above the parameter
What can one say about the sampling distribution of the sample proportion, assuming the samples taken were simple random samples?
its standard deviation is (0.5)x(1/sqrt(n))
A 1996 Gallup poll of eligible New Hampshire primary voters reported that "of 1200 voters surveyed, 24% would vote for Senator Bob Dole if the primary election were held today". The Gallup organization also reported that the margin of error for a sample of 1200 people is 3 percentage points. If the Gallup organization had wanted to make a confidence statement based on the same data, only with more confidence that the interval had captured the parameter, what do you think would happen to the margin of error? It would be
larger than 3%
A Gallup poll found that "with the presidential election less than a month away, 28% of Americans are satisfied with the way things are going in the U.S." The Gallup organization also reported that the margin of error for a sample of 1200 people is 3 percentage points. If the Gallup organization had wanted to make a confidence statement based on the same data, only with more confidence that the interval had captured the parameter, what do you think would happen to the margin of error? It would be
larger than 3%
You ask a question to a random sample of 1500 adults in Texas (population 18 million people) and to a separate random sample of 500 adults in Indiana (population 5.7 million people). You make separate 95% confidence statements about the percent of all adults in each state who agree. Your margin of error for Indiana is
larger than in Texas, because there are fewer people in the Indiana sample.
If you want a 95% margin of error to be 1%, what will your sample size have to be?
n=10000
In a 2012 Gallup poll, eighty-two percent of adult U.S. Catholics say birth control is morally acceptable. Results for this poll are based on telephone interviews conducted May 3-6, 2012, with a random sample of 1,024 adult Catholics, aged 18 and older, living in all 50 U.S. states and the District of Columbia. In this situation, the 1024 adults are the
sample
You ask a question to a random sample of 1000 adults in Texas (population 18 million people) and to a separate random sample of 1000 adults in Indiana (population 5.7 million people). You make separate 95% confidence statements about the percent of all adults in each state who agree. Your margin of error for Indiana is
the same as in Texas, because the two samples are the same size.
