STATS 210 Final Exam

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

Exhibit 1, Question 2: Which of the following is a source of circumstantial evidence that was cited in the article as further support of a link between pancreatic cancer and coffee?

About 10 years ago, a British cancer journal reported an association between coffee consumption and pancreatic cancer in a study correlating trade statistics and cancer in 20 countries.

If we are testing the hypothesis H0: p ≤ 0.35 versus HA: p > 0.35 and we compute z to be 0.04, then what can you say? A copy of the Standard Score Table is provided

we fail to have convincing evidence that p is > 0.35

Suppose you are testing H0: p = p0 vs. HA: p ≠ p0. If you get a z value (standard score) of 2.01, what is the corresponding p-value for this test? A Standard Score Table is provided.

0.04

Let A = Ottawa Ankle Test Says Ankle is Broken; and B = Ankle Really is Broken. Suppose you know the following. P(A|B) = .8; P(A) = .4; P(B) = .3. What is P(B|A)? Use Bayes Rule.

0.60

In the context of screening tests, specificity is the same as:

1 - The false positive rate

The correlation coefficient is always:

Between -1 and 1

Read the following article on pagoclone. What HA is being tested?

HA: pagoclone is better than a placebo

What is the "negative predictive value" of a screening test?

It is the probability the condition is really absent, given the test came back negative.

What do we mean by "human inference?"

Off-hand phrase taken to mean inference we make from statistical constructs

Suppose A = "condition is really present," B = "test says condition is present," C = "condition is really not present, " and D = "test says condition is not present." In symbols, what is analogous to the false positive rate of the test?

P(D|C)

Read the article by Dr. Justin Lehmiller, below.This difference in distance they refer to was said to be "statistically significant" in a follow up to this article. What does the author say about practical significance in this study?

The author doubts that six or seven inches difference is any real evidence of fidelity.

What is a Type II error most analogous to?

false negative

Exhibit 1, Question 1: What is the value of r?

r = -0.44

Exhibit 2, Question 1: What is the value of r?

r=-0.80

The CEO of a large electric utility claims that more than 80 percent of his customers are very satisfied with the service they receive. To test this claim, the local newspaper surveyed 1000 customers, using simple random sampling. Among the sampled customers, 83% say they are very satisfied. We want to decide if the 83% is enough evidence to lead us accept or reject the CEO's claim. What is the standard score associated with a test of the hypothesis H0: p ≤ 0.80 vs HA p > 0.80? A standard score table is provided

2.37

in a study reported in the Chicago tribune, in 2012, twenty four students were fatally shot during the school year that ended June 15, four fewer than in the 2010-11 ear. but the overall shooting toll-319- was the highest in four years and nearly 22 percent increase from 2011. what was the total number of shootings in 2011?

261

Let's assume you have developed a model designed to screen for the stability of banks and predict bankruptcy. So your model is designed to "sound an alarm" if it predicts a bank will become bankrupt (a "positive"). To test how well you model is working, it was applied to 3000 banks, 286 of which were known to have gone bankrupt and 2714 of which remained solvent. The data collected from the study are in the 2x2 table below. Please answer the following questions in the spaces provided. What is the specificity of your model?

2689/2714

a precinct has 42,128 registered voters, 40 percent democrat, 60 percent republican. An SRS of 100 (yielding 72 democrats and 28 republicans) are asked: "do you oppose using rabid squirrels to protect our southern border?" 50% of the republicans (14) say "yes" and 75% of the democrats (54) say "yes". if the estimated of all registered voters in this precinct who would say "yes" to this question is reweighted to reflect the distribution of republicans and democrats in the precinct population, what would it be in this case (approximately)?

60%

the distribution shown here represents the sampling distribution that resulted from 44 simple random samples, each of size 50, taken from a manufactured population of 250 voters. in each case the proportion of sampled voters who agreed the government was doing enough about the problem of rabid squirrels was recorded. about what percentage of the time did a sample percentage between 25% and 40% occur?

64%

this question concerns the sampling distribution of a sample proportion (shown below). if you know that 38% of all sample proportions will fall within 0.5 standard deviations from the parameter p, what is the 38% margin of error for a sample of size 400?

0.0125

A sample of n = 200 U.K. students is taken and each one is asked "Does knowing that many of the basketball players U.K. recruits will go pro after one year affect your sense of attachment to the team?" Suppose 55% in your sample said "yes, it does affect my attachment." You want to know if it is safe for the Kernel to report that a majority of all U.K. students are likely to feel that way. So your job is to decide between H0: p ≤ 0.50 and HA: p > 0.50, where p is the true proportion of all UK students who would have said "yes" had all been asked. What is the p-value (more or less) associated with this decision? A Standard Score Table is provided.

0.08

suppose you have a small population of twenty marbles, 8 of which are blue, 3 red, 6 green, and the rest yellow. suppose you were to list all possible samples of size 3 marbles from this population and, in each case, compute the sample proportion of each set of 3 that were yellow. if you then added up all those sample proportions (there are 1140 of them) and divided by 1140 what would you have to get?

0.15

please read the following article from CBS news. What is the sample for the CBS news poll?

1,110 adults contacted by phone

In the New York Times Magazine, Tara Parker-Pope makes the case that teenagers are more conservative than their parents were. For example, the fraction of high-school seniors who reported that they had recently consumed alcohol fell from 72% in 1980 (illustrated as the big one-gallon - 128 ounce - jug) to 40% in 2011 (illustrated as the little 8-ounce glass). The actual percent "Parents" consumption divided by percent "Kids" consumption is approximately _____ but the graphic makes that ratio look more like _____. The two best answers for filling in these blanks (in respective order) are:

1.8 and 16

A (real) test was constructed as a way of checking to see if Retinal Vein Pulsation (RVP) was reliable as a test for Intracranial Pressure (IP). The absence of RVP is considered to be indicative of dangerous IP. So the test looks for absence of RVP and in that sense "absence" is a "positive" outcome. A study enrolled 189 patients and each patient was given this RVP test. Results of the testing, along with a categorization of High or Normal IP is in the table. What is the negative predictive value of this test?

100%

what sample size would you have to take if you wanted a 99.9% margin of error of 1/2 of 1 percent?

108,241

A (real) test was constructed as a way of checking to see if Retinal Vein Pulsation (RVP) was reliable as a test for Intracranial Pressure (IP). The absence of RVP is considered to be indicative of dangerous IP. So the test looks for absence of RVP and in that sense "absence" is a "positive" outcome. A study enrolled 189 patients and each patient was given this RVP test. Results of the testing, along with a categorization of High or Normal IP is in the table. What is the false positive rate of this test?

12%

In BN 2.29 you studied about the role of incentives and whether they mattered. table 2.10 recorded the results of the Earl Response incentive. what two percentages would you use to evaluate the effect of "$30 incentive" versus "no incentive" on early response?

16% and 34%

You plan to take a sample of 200 voters in Kentucky and ask "Do you think NSA leaker Edward Snowden should be considered a hero?" How likely is it that your sample proportion of "yes" answers is no more than 0.035 away from the true proportion of all voters in Kentucky who would have answered yes to this question, had they all been asked? The graphic here may be of some assistance.

68 chances in 100

the recent poll of 1200 college age students found that 88 agreed with U.S. foreign policy toward Russia. what is the corresponding 95% confidence interval (choose closest answer)? the following information may be of help to you.

7% plus or minus 3%

A new test is developed for the detection of carcinoma of the prostate.(Foti et al. N Engl. J Med. 1977). When it is tested in a group of 113 patients with prostatic cancer, 79 have a positive test. In a group of 217 individuals without prostatic cancer, 10 have a positive test. What is the sensitivity of the test?

70%

A new test is developed for the detection of carcinoma of the prostate.(Foti et al. N Engl. J Med. 1977). When it is tested in a group of 113 patients with prostatic cancer, 79 have a positive test. In a group of 217 individuals without prostatic cancer, 10 have a positive test. What is the positive predictive value of the test

89%

please read the following article from CBS news, this survey reports a margin of sampling error of about 3%. using the formulas for MOE you learned in this class; what level of confidence does this MOE correspond to?

95%

In Excel what is the function for finding the correlation coefficient? Google on this if you don't know.

=CORREL( )

Exhibit 2, Question 2: The hospital is more likely to adopt a quasi-design that collects data for an extended period of time before hand cleaner dispensers are installed,and then compares those findings with data collected after the dispensers are installed. Which of the following is a source of confounding that might occur with this kind of design?

All of these answers are correct

what is a cross-sectional sample?

An attempt to match the sample characteristics exactly to those of the population

Exhibit 1, Question 2: Does the scatterplot show a positive association or a negative association, and how do you know?

Association is negative (because scatterplot is downwards to the right).

Exhibit 2, Question 2: Does the new scatterplot show a positive association or a negative association, and how do you know?

Association is negative (because scatterplot is downwards to the right).

In this class we relegated all confounding to two possible sources. What were those?

Improper comparison and lack of randomization

We looked at a study that showed college students who ate breakfast had a higher success rate on General Biology exams than those students who did not eat breakfast. The operative graph is repeated below. What does the graph tell you?

Eating breakfast is associated with better class performance.

What is a "quasi experiment"?

Experiments unable to use randomization to evaluate treatment effectiveness.

Read the following excerpt from the Washington Post. The words "statistically significant" are used. What H0 is being tested?

H0: Vouchers don't help graduation rates

Please read the article here on the libido drug Flibanserin. Was the alternative accepted or not? How do you know?

HA was accepted, because the results were statistically significant

Read the following excerpt from the Washington Post. The words "statistically significant" are used. Assuming Mr. Wolf is using those words correctly, what seems to have been chosen during his study, an H0 or an HA?

HA, since that is always what statistical significance implies

Recall the article about the Harris Poll that was discussed in one of our BN assignments. 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

Two variables measured on the same individual are ASSOCIATED if:

If some values of one of the variables tend to occur more often with certain values of the second variable than with other values of that variable

Why did Subway stop using azodicarbonamide in its breads?

It (or its breakdown products) was found to cause cancers of the lung and blood vessels in mice.

We used the concepts of sensitivity and specificity to create a transition from concepts that were familiar, to formal hypothesis testing, which was less familiar. In this transition we chose to view a hypothesis as a screening test. In that context of testing H0 versus HA, what does it mean to have a "false positive"?

It means you would conclude HA is true when really H0 is.

A plot very similar to the one shown here was allegedly presented to the Kentucky House of Representatives as part of an overall message that an increase in CO2 emissions causes a decrease in child mortality rates. What would you say in response to this argument?

It's irrational; the pairing of high C02 emissions with low mortality rates only shows an association. There is no evidence of direct cause and effect.

Please read the following article on antivirus software. What do you think the article means by detection rate?

It's like "sensitivity" - the ability to identify a positive (virus) correctly.

A plot very similar to the one shown here was allegedly presented to the Kentucky House of Representatives as part of an overall message that CO2 emissions are negatively associated with child mortality rates. What would you say in response to this argument?

It's reasonable; low C02 emissions are somewhat paired with high mortality rates.

Do you think the computation of r is appropriate for these data? Why or why not? (You constructed a scatterplot of these data in Beyond the Numbers 1.27.)

Makes much more sense for these data since the transformed plot looked much more like a straight line.

Exhibit 2, Question 1: The article addresses amyotrophic lateral sclerosis (ALS), suggesting that mice studies might be misleading. The article gives two reasons why. One of those is:

Mice in the studies tended to die from bowel-related issues while in humans it is almost always muscle wasting.

Exhibit 1, Question 1: Based solely on the graph, could you say eating breakfast and student performance have a cause and effect relationship? Explain.

No. From the graph we only know they are associated and association does not imply causation.

Exhibit 1, Question 1: What two groups were being compared in this experiment?

Pancreatic cancer patients and patients hospitalized for reasons unrelated to their pancreas.

Exhibit 1, Question 2: Which of the following is another plausible reason why the inference in Question 1 might be compromised?

Pretest scores suggest those enrolling in the online course were notably better prepared for the course than those in the traditional class.

Exhibit 1, Question 3: Is the association weak or strong, and how do you know?

Pretty strong. Points are pretty tightly packed about the curvy trend we see in the plot.

Exhibit 1, Question 3: Do you think the computation of r is appropriate for these data? Why or why not?

Probably not. That plot was not a straight-line plot so r might be deceptive here.

You plan to take a sample of 2000 voters in Kentucky and ask "Do you think former Cambridge Analytica employee Chris Wylie should be considered a hero?" You take your sample and have a sample proportion of 75% who say they think Wylie should be considered a hero. If you are choosing between 𝐻0: 𝑝 ≤ 0.73 𝐻𝐴: 𝑝 > 0.73 what decision do you make and why? Take α = 0.05. Use the Standard Score Table that is provided.

Reject H0 with a p-value less than 0.05

What is the Delaney Clause ("Amendment")?

Says that if a substance causes cancer in animals then it can't be considered safe for use in food products.

If you compute a correlation coefficient to be -0.26 what does that tell you about the scatterplot, all things being equal?

Should be a recognizable, though not strong, downward to the right trend

Exhibit 1, Question 2: Which of the following is a plausible reason why the inference in Question 1 might be compromised?

Students got to self-select, that is decide for themselves which course they enrolled in.

Recall the online learning study you read about in BN 1.14. What was one obvious source of confounding that threatens the article's conclusion that online learning is no less effective than face-to-face learning?

Students got to self-select; that is to decide for themselves which course (online or face-to-face) they enrolled in.

Exhibit 2, Question 1: Reportedly, the Legislature was told that this graph shows that global warming is good because it causes a decrease in infant mortality. Is this an accurate assessment? Explain.

That is really not a correct explanation. The graph shows only correlation, not causation. Probably it is how industrialized the nation is that affects both carbon footprint and infant mortality. Certainly it is not saying that a large carbon footprint is directly responsible for a reduction in infant mortality.

Exhibit 1, Question 1: Looking at the Results section, what inference are you likely to make about the effectiveness of online instruction?

That online instruction was no worse than face-to-face instruction

A sleep study was done in Stockholm in 2010 to investigate whether sleep deprived people are perceived as less attractive (no kidding). 23 healthy, sleep deprived adults (age 18-31) were photographed after a normal night' sleep (8 hours) and after 31 hours of sleep deprivation. The photographs were presented in random order to 65 untrained observers (age 18-61) who rated them. The sleep deprived photographs were rated on average as less attractive than those taken after the normal night's sleep, and this result rose to the level of statistical significance. What was H0

That sleep deprived photos and normal sleep photos were equally attractive

Read the article by Dr. Justin Lehmiller, below. This difference in distance they refer to was said to be "statistically significant" in a follow up to this article. What does statistical significance mean in the context of the article?

That the physical distance men stayed from the "attractive woman" was enough larger for the oxytocin men than for the placebo men that it was likely not due to chance.

We looked at a study that showed college students who ate breakfast had a higher success rate on General Biology exams than those students who did not eat breakfast. The operative graph is repeated below. The study was done on 1,259 college students, 825 of whom self-identified as having eaten breakfast before taking the exam. What can you say about the number of students who got D's and E's in each of the two groups?

The Breakfast group had more D's and E's

Read the following excerpt from the Washington Post. What does the claim of statistical significance have to do with a kind of false positive rate

The FPR is essentially the same as an assumed Type I error rate, typically taken to be 0.05. In this case, the p-value must have been smaller than 0.05

Exhibit 2, Question 2: A 1958 amendment to the Food,Drugs, and Cosmetic Act of 1938 called the "Delaney Clause" has been instrumental in the banning of food additives since its enactment. What is the text of the one-sentence Delaney Clause?

The Secretary of the Food and Drug Administration shall not approve for use in food any chemical additive found to induce cancer in man, or, after tests, found to induce cancer in animals.

In the context of hypothesis testing, good sensitivity refers to:

The ability of the test to reject an H0 that is false

Exhibit 1, Question 2: Aside from randomization issues, which of these is another possible source of confounding that might challenge the conclusion that exposure to music caused the L.A. students to do better.

The control group in Orange County had both traditional and automated mathematics instruction (not just automated).

Exhibit 2, Question 1: Although this article doesn't describe an experiment, it does imply that being a little overweight may lead to a longer life. Which of the following is a plausible confounding variable that may compromise the validity of this inference?

The presence or absence of disease in subject (person) being studied.

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, with some statistically rough language: "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?

The 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

A plot very similar to the one shown here was allegedly presented to the Kentucky House of Representatives as part of an overall message that related CO2 emissions to child mortality. How did taking log base 10 of each variable shown, and making a new plot, make using "r" more reasonable for measuring association?

The transformed scatterplot went from showing a curved trend to showing a straight line trend.

How do you know that the subjects in the Brains and Beats study (BN 1.15) could not have been randomized to the treatments that were compared? This was one of the more widely-reported studies that supported music training as positively impacting general academic performance.

The treatments were at two separate schools at two separate points in time.

In BN1.16 (or on the video version) on Comparison and Randomization we discussed an aids drug (Ribavirin) that the FDA ended up rejecting. What was wrong with the experimental design that the company used?

There was evidence that the sickest patients had been assigned to the placebo group.

Exhibit 1, Question 1: How do you know that the subjects in this study could not have been randomized to the treatments that were compared?

They couldn't have been randomized. The treatments were at two separate schools at two separate points in time.

Exhibit 2, Question 1: Redo the scatterplot from Exhibit 1. Same rules as before: use a computer package and submit professional-level results. This time, plot log10 (Child Mortality) versus log10 (CO2 Emissions). How does this plot compare to the one you did in Exhibit 1?

This one is much more in the shape of a straight line than the original one from Exhibit 1.

What is the legal analogy to an alpha level?

Threshold for reasonable doubt

Exhibit 2, Question 1: Suppose a researcher suggests to place these cleaners in randomly chosen patient rooms and not in others. At the end of the study, the infection rates for each group could be compared. Why might this be an impossible design to implement in practice?

To quote the paper "it is difficult, politically, to implement use of an alcohol-based disinfectant only in certain parts of a hospital or only on certain sides of a ward." It would also be hard to manage. If a health care worker knows the hand cleaner is in room 101 then she may well stop in there and grab some before going to tend to a patient in room 102, where no cleaner has been made available.

Suppose we have data like in Problem 4 that can be into a so-called 2x2 table like you see below. The letters U, V, W, X just stand for the counts that are in those cells. What is the probability of getting a Grade of C or Better if you ate breakfast, divided by the probability of getting a Grade Below C if you ate breakfast?

U/V

In our class what do we mean when we say the results of a certain test are "not statistically significant"?

We mean we have not been able to reject H0 with a Type I rate that is tolerable (usually 0.05)

in a 2012 Washington post article entitled "is college too easy as study time falls, debate rises," Daniel de Vise reports that "over the past half century, the (average) amount of time college students actually study-read, write and otherwise prepare for class-has dwindled from 24 hours a week to about 15.." no standard deviation is given, but let's assume that standard deviation is 2.5 hours. suppose a college student is selected at random. use the empirical rule to estimate how likely it is that this student studies between 12.5 and 20 hours per week. the graphic below may be of some help to you

about 81.5 chances in 100

Look at the sampling distribution plot shown below. This is the sampling distribution of the sample proportion. For samples of size 400, about what percentage of all sample proportions will be in the interval (p-0.05, p+0.025)?

about 81.5%

please read the following article from CBS news. what is the population for the CBS news poll?

all adult Americans

a dean of admissions at U.K. once tallied up the ACT scores for ALL entering freshman for that year and reported that the average was 25. He then attached a margin of error to that number. A faculty member objected to this, arguing that it didn't make sense. this faculty member is:

correct, because the Dean's figure was the parameter and not subject to any sampling variability

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%. a faculty member in the audience claimed this was not appropriate. that faculty member was:

correct, because the margin of error has nothing to do with biased questionnaire designs

We worked a fair amount with data from the NHTSA's 1998 San Diego field sobriety test validation study, issued by the agency as the report "Validation of the Standardized Field Sobriety Test Battery at BACs Below 0.10 Percent," by Drs. Jack Stuster and Marcelline Burns. In several of our exercises we used the total number of infractions as the way in which the test would flag someone as potentially drunk. Suppose the total infractions needed to say you are likely drunk is changed from 2 or more to 5 or more. What will happen to the specificity of the test as a result of this change?

increases

a student stands out in front of whitehall classroom building and asks the question "are you in favor of spending millions of dollars to renovate whitehall" to the first 100 students she feels comfortable stopping. what can one say about the sampling distribution of the sample proportion from this person's sample?

is is about the bell shaped and peaks above the parameter

What can one say about the sampling distribution of a sample statistic based on a simple random sample?

it is about the bell-shaped and peaks above the parameter

you have a set of 10 data points all between 45 and 50. then number 1000 is added in as the 11th data point. what is the standard deviation of the new (eleven item) data set compared to the standard deviation of the original (ten item) data set?

larger than it was before

what does the word "parameter" refer to in statistical science?

number that describes the population

what kind of error does the margin of error address?

random sampling error

suppose there are 9 people on a bus in Seattle and the average of their yearly income is $65,000. at the next stop, the highest paid person on the bus (with an income of $120,00 per year) gets off and Bill Gates gets on. Mr. Gates makes 7.6 billion dollars a year. what is the new median salary of the people on the bus?

same as it was before

Gastric freezing used to be used as a treatment for stomach ulcers. Physicians justified the use of this treatment based on interviews with patients, pre and post treatment that revealed an improvement, on average, in patient discomfort. The problem with this experimental design was that

the design did not allow any placebo comparisons

Confounding often defeats attempts to show that one variable causes changes in another variable. Confounding means that

the effects of two or more variables are mixed up, so we cannot say which is causing the response

suppose you have a data set with 1000 observations in it. 500 of those are all 5 and 500 are 15. what of the following are true?

the median are the same

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

Reporting the results of a medical experiment, researchers claim that the difference between two headache treatments is "statistically significant." What is the null hypothesis here?

the two headache treatments perform equally well

what is sampling variability?

the variability seen in statistics from sample to sample

If someone reports a p-value of 0.05 when testing a hypothesis with an assumed Type I error rate of 0.001, then we can say that

there's only 1 chance in a 1000 that going with the alternative will be a mistake.

what is the goal of sampling?

to make inferences about a population from what we know about our sample

What do we mean by statistical significance?

treatment differences that are sufficiently large that you can say they are unlikely to have happened by chance;

please read the following article from CBS news. the headline on this article refers to the "majority of Americans." assuming this means "All Americans" is the headline statistically defensible?

yes, because 54% =/- 3% does not overlap 50%; so you are, in a sense, 95% sure that p is bigger than .5 (50%)