2.2 - 5.1 (exam 2 reviews)
If your risk of a disease is 2% without getting vaccinated, and 0.2% if you get vaccinated, the relative risk of disease if you don't get vaccinated is
(2/0.2) = 10
As part of a class project, a student conducts a survey of 50 students at her school finding that, on average, the students in the sample report spending 2.3 hours per day watching TV (SD=2). The student wonders if this is significantly less then the national average of 4.9 hours per day. The parameter of interest in this study is
The average hours per day spent watching TV among all students at the school
Relative risk is the ratio of two conditional proportions. It indicates how many times more likely on event will happen as compared to another.
True
As the confidence level increases (90% to 95% to 99%), the width of the confidence interval increases because the more sure we are that we have captured the true answer, the wider our net must be.
true
Suppose that the score that is a 1 was a mistake and was supposed to be 4. If we corrected this entry in the dataset, how would the following numerical statistics change, if at all?
- the mean would be larger - the median would be the same
What type of error occurs when a false null hypothesis is not rejected?
Type 2
What type of error represents a missed opportunity?
Type 2
True or False? In a two proportion (or two mean) study, if the confidence interval contains zero, the study is not significant. Hint: Remember, confidence intervals are plausible values for the population. So if the null (zero) is a plausible (or possible) value in the population ...
True
A 2013 Gallup poll asked randomly selected U.S. adults whether they wanted to stay at their current body weight or change. One purpose was to investigate whether there was any difference between men and women with regard to this aspect. What is the test statistic in context of this study?
the proportion difference between men and women who wanted to stay at their body weight
The researchers obtained a random sample of 500 adult Americans and reported that 65% of the participants in the sample supported gun ownership. A theory-based 90% confidence interval for the true proportion of all adult Americans who support gun ownership is
(0.6149, 0.6851)
Observational studies are able to determine cause-effect conclusions between the explanatory variable and the response variable
False
The mean is resistant to extreme values
False
Suppose that you perform a significance test using the α = .05 significance level. You would reject the null hypothesis for values less than or equal to .05.
True
The standard deviation is resistant to extreme values
False
Which factor affects p-values and confidence intervals? Select one: a. The larger the difference between the sample proportions (or means), the stronger the evidence that the population proportions (or means) differ. This p-hat or x-bar will be in the center of the confidence interval. b. Larger sample sizes produce stronger evidence that the population proportions (or means) differ. It also produces narrower confidence intervals. c. They are both factors d. Neither one is a factor.
C. They are both factors
A student participates in a Coke versus Pepsi taste test. She claims that she can reliably tell the difference between the two soft drinks. We want to run the appropriate test of significance to see if she can correctly identify the soft drink the majority of the times. Which of the following describes the Type I error in this study?
In reality she is just randomly guessing the type of drink (so her probability of making a correct guess is 50%) but we concluded that her probability of correctly identifying the type of drink is more than 50%
The researchers obtained the salaries of a random sample of 200 full professors of colleges in the United States. The sample mean is =$73,820, and the sample standard deviation is $6,800. We will assume that the distribution of the sample data is not extremely skewed.The researches want to know if there a significant evidence that the long-run average salary of all full professors of colleges in the United States is less than $75,000. What are the null and alternative hypotheses?
Null hypothesis: the long-run average salary of all full professors of colleges in the United State is $75,000 Alternative: the long-run average salary of all full professors of college in the United States is less than $75,000
Changing the sample size impacts the width of the confidence interval. Generally speaking (if the sample statistic remains the same) a 95% confidence interval's width will decrease the larger the sample size.
True
The approximate 2SD method for a 95% confidence interval for a population proportion is only valid when the validity conditions are satisfied.
True
In what type of study do neither the researcher nor the subject know which treatment is being used on each subject?
double-blind
Researchers want to assess whether a new drug is more effective against a disease than a placebo, and so they conduct a randomized experiment in which volunteers are randomly assigned to receive a placebo or the new drug. Researchers keep track of whether or not the person still has the disease after 2 weeks. In this study cause-and-effect conclusions are
potentially possible
The margin of error (+/- a number) decreases (gets smaller) when...
- sample size increase - standard deviation decrease - confidence level decrease
Power, the ability to detect significance, is a function of alpha (Type I error)
False
True or False. The 3-S strategy is no longer applicable when testing hypotheses about two group proportions.
False
True or False. The simulation strategy when comparing two group proportions involves flipping coins.
False
Let π denote some population proportion of interest and suppose a 95% confidence interval for π is calculated to be (0.6, 0.7). Also, suppose that we want to run the following two-sided test of significance Ho: π = 0.63 Ha: π ≠ 0.63 What can you definitely say about the corresponding p-value?
The corresponding p-value will be larger than 0.05
When a sample is large enough, variability is reduced. This is a good thing.
True
When a study involves two categorical variables what can the data be organized in?
Two-way table
Jane is doing an experiment to determine whether the amount of time a person spends reading affects their SAT score. After a few of the subjects come to the lab and read for a certain amount of time, one of the lamps burns out and therefore makes the lab much darker for the rest of the subjects. In this example, the amount of light is what type of variable?
confounding variable
Relative risk can only be performed on
two proportion samples
As part of a class project, a student conducts a survey of 50 students at her school finding that, thirty-eight of the 50 students (76%) reported owning a smartphone. The student conducts a two-sided test of the null hypothesis that the true proportion of students at her school with a smartphone is 50%. This test yields a p-value of <0.001. If the student instead conducts a two-sided test of the null hypothesis that the true proportion of students at her school with a smartphone is 75% she obtains a p-value of 0.99. We can conclude that
75% is one plausible value for the true proportion of students at her school with a smartphone
In a recent survey a Statistics course instructor asked her students how many hours per week they expected to spend studying statistics outside of class. Forty-nine students responded to that question, with an average of 8.2 hours and a standard deviation of 3.8 hours. The data were not strongly skewed so the instructor constructed a theory-based confidence interval for these data. The interval is (6.7440, 9.6560). The confidence level used for this interval is
99%
As part of a class project, a student conducts a survey of 50 students at her school finding that, on average, the students in the sample report spending 2.3 hours per day watching TV (SD=2). The student wonders if this is significantly less then the national average of 4.9 hours per day. The t-statistic for this data is given as -9.19, and the p-value for this test of significance is <0.001. Based on the standardized statistic and p-value, it is possible that the researchers will have made
A type I error (false positive)
With quantitative data, another factor that will impact the confidence interval is the margin of error and standard deviation. Generally speaking (with fixed sample size and 95% confidence interval), the larger the standard error or deviations, the larger the width of the confidence interval.
True
What type of error occurs when a true null hypothesis is rejected?
Type 1
A student participates in a Coke versus Pepsi taste test. She claims that she can reliably tell the difference between the two soft drinks. Let represent the long run probability that the student can identify the soft drink correctly. We decided to run the appropriate test of significance to see if she can correctly identify the soft drink the majority of the times. H0: = 0.5 Ha: > 0.5 The p-value of our test is 0.08. Which 95% confidence interval for the values of makes sense?
[0.4, 0.6]
As part of a class project, a student conducts a survey of 50 students at her school finding that thirty-eight of the 50 students (76%) reported owning a smartphone. If the sample size increased from 50 students to 100 students, the margin of error for the confidence interval would
decrease / get smaller
A researcher finds that among a random sample of teenagers, those who watched more TV as children are more likely to have lower IQs as teenagers and concludes that "Watching TV as children causes your IQ to decline". This conclusion is
misleading based on the study design
What is a study in which the researcher actively assigns subjects in the sample to treatment groups and something is done to them.
experiment
The theoretical stipulations or validity conditions for a one-sample t-test is that there must be at least 20 observations AND that there must be a fairly symmetric distribution.
True
The median is resistant to extreme value
True
A confounding variable is
associated with both response variable and explanatory variable
A confidence interval will increase in width if:
either the sample size decrease or the confidence level increases
A sample was taken of the verbal GRE scores of 19 applicants to graduate school at a large Midwestern university. Below are the scores: (For convenience, the data are ordered) 280 310 340 350 370 410 420 420 420 470 490 510 520 520 600 610 670 720 750 The median applicant score is
470
As part of a class project, a student conducts a survey of 50 students at her school finding that, thirty-eight of the 50 students (76%) reported owning a smartphone. The student conducts a two-sided test of the null hypothesis that the true proportion of students at her school with a smartphone is 50%. This test yields a p-value of <0.001.We can conclude that
50% is not a plausible value for the true proportion of all students at the school who own a smartphone
You are using the randomization approach (α = .10). Indicate whether you would reject the null hypothesis at the .10 significance level. (A).078 ( B) .045 (C) .0001 (D) .051
All of them would be rejected; all are significant
The researchers obtained the salaries of a random sample of 200 full professors of colleges in the United States. The sample mean is =$73,820, and the sample standard deviation is $6,800. We will assume that the distribution of the sample data is not extremely skewed. The researches want to know if there a significant evidence that the long-run average salary of all full professors of colleges in the United States is less than $75,000.
Can the results of the test be generalized to the population of all full professors of colleges in the United States? -- Yes
Are cuteness and aggression related? A Yale University study tested this by showing people pictures of cute animals (like kittens and puppies) and pictures of older more serious looking animals. They tested the aggression of the subjects by giving them bubble wrap and let them pop the bubbles. The researchers kept a record and compared the average number of times the subjects in each group popped the bubbles after looking at their respective pictures. What is the Explanatory / Independent and the Response / Dependent variables?
Explanatory variable - Cute factor: cuddly, young animals vs older, serious animals Response variable - number (or average) of bubble-wrap bubbles popped
As part of a class project, a student conducts a survey of 50 students at her school finding that, thirty-eight of the 50 students (76%) reported owning a smartphone. True or False. If the validity conditions are not met, you should use a theory-based method, not a simulation based method of computing a confidence interval.
False
True or false. The purpose of random assignment is to ensure that the sample is representative of the population.
False
A study found that college students who live off -campus are significantly more likely to drink alcohol than those who live on-campus. Two questions: Is this an observational study or an experiment; and Is it appropriate to conclude that living off-campus causes a student to be more likely to drink alcohol?
Observation, no, it is not appropriate to conclude causation; only strong association
As part of a class project, a student conducts a survey of 50 students at her school finding that, on average, the students in the sample report spending 2.3 hours per day watching TV (SD=2). The student wonders if this is significantly less then the national average of 4.9 hours per day. The p-value for this test of significance is <0.001, thus the student should
Reject their null hypothesis at the 0.05 significance level
Suppose I am conducting a test of significance where the null hypothesis is that a student will pick the right front tire 25% of the time and the alternative hypothesis is that the student will pick the right front tire at a rate different than 25% when asked to randomly pick a tire position on a car. H0: π = 0.25 Ha: π ≠ 0.25 I end up with a p-value of 0.033. I also construct 95% and 99% confidence intervals from my data. What will be true about my confidence intervals?
The 95% interval will not contain 0.25, but the 99% interval will contain 0.25
When evaluating a null hypothesis that disease risk is the same between a treatment and placebo group, one choice for the statistic to use when implementing the 3-S strategy is
The difference in the proportion of diseased individuals between the treatment and placebo groups
In a Professor's statistics class, there were 20 males and 10 females, 5 of the males have A's, but only 4 of the females have A's. In order to evaluate whether there is an association between sex and getting an A in his class he should compare
The fact that 5/20 males got A's and 4/10 females got A's
Which of the following statements is true?
The median might be smaller or larger than the mean, depending on the shape of the data
In Exploration 1.1, we looked at a study to investigate whether a dog could select the correct cup more than 50% of the time in the long run. Which of the following would be a Type I error.
The researcher concludes that the dog can communicate with humans -- that he is not guessing, when in fact, he was only guessing
As part of a class project, a student conducts a survey of 50 students at her school finding that, on average, the students in the sample report spending 2.3 hours per day watching TV (SD=2). The student wonders if this is significantly less then the national average of 4.9 hours per day. The t-statistic for this data is given as -9.19. This means that
There is very strong evidence against the null hypothesis
The randomization method uses the equation: p̂ ± 2 x (SD of the null). The theoretical method uses the equation: p̂ ± multiplier x (SD of the null).
True
True or False. The following two statements are equivalent when referring to a study comparing a new drug to a placebo and its effect on disease risk (disease risk=proportion of diseased individuals) a. Disease risk when receiving the placebo is equal to disease risk when receiving the new drug b. There is no association between the group someone is in (placebo or new drug) and disease risk
True
newspaper conducted a statewide survey concerning the 1998 race for governor. The newspaper took a simple random sample of 1200 registered voters and found that 640 would vote for the Democratic candidate.The researchers run a test of significance to see if there is strong evidence that a clear majority of the population would vote for the Democratic candidate? The p-value of the test of significance is .02 and the power of this test was 80%. The researchers used significance level 5%. The conclusion was made to reject the null hypothesis. What type of error could have been made?
Type I error
As part of a class project, a student conducts a survey of 50 students at her school finding that, on average, the students in the sample report spending 2.3 hours per day watching TV (SD=2). The student wonders if this is significantly different than the national average of 4.9 hours p/day. The p-value for this test is <0.001. If the student decides not to compute a 95% confidence interval and instead computes a 99% confidence interval instead, this interval will be
Wider than the 95% confidence interval
The researchers obtained the salaries of a random sample of 200 full professors of colleges in the United States. The sample mean is =$73,820, and the sample standard deviation is $6,800. We will assume that the distribution of the sample data is not extremely skewed. Th researches want to know if there a significant evidence that the long-run average salary of all full professors of colleges in the United States is less than $75,000. Are conditions for the appropriate theory-based test of significance met? Explain your reasoning:
Yes, the validity conditions are met because the sample size is at least 20 and the distribution of the sample data is not extremely skewed
In August 1998, an article titled "Prayer Can Lower Blood Pressure" appeared in the USA Today. The article was based on the findings of a study by the National Institutes of Health Initiatives that followed 2,391 people aged 65 years or more. The article said: "People who attended a religious service once a week and prayed or studied the Bible once a day were 40% less likely to have high blood pressure than those who don't go to church every week and prayed and studied the Bible less." What is a confounding variable?
being active impacts blood pressure (treatment)
The researchers obtained the salaries of a random sample of 200 full professors of colleges in the United States.The sample mean is $73,820, and the sample standard deviation is $6800.A theory-based 95% confidence interval for the average salary of all full professors of colleges in the United States is
(72871.8200 , 74768.1800)
As part of a class project, a student conducts a survey of 50 students at her school finding that, thirty-eight of the 50 students (76%) reported owning a smartphone. The student finds a 95% confidence interval to be 64% to 88%. What is the margin of error for this confidence interval?
(88 - 64)/2 = 12%
As part of a class project, a student conducts a survey of 50 students at her school finding that, on average, the students in the sample report spending 2.3 hours per day watching TV (SD=2). The student wonders if this is significantly different than the national average of 4.9 hours p/day. The p-value for this test is <0.001. A 95% confidence interval is computed for the average hours per day spent watching TV among students at the school. Based on the information provided in previous questions this interval...
- Will not include 4.9 - Will include 2.3
Generally speaking, the median is
- larger than the mean if the data is left skewed. - smaller than the mean if the data is right skewed
As part of a class project, a student conducts a survey of 50 students at her school finding that, on average, the students in the sample report spending 2.3 hours per day watching TV (SD=2). The student wonders if this is significantly less then the national average of 4.9 hours per day. Which of the following is a type II error
Concluding there is not enough evidence to say that the average daily TV watching at the school is less than the national average, when it actually is
A drug company wants to test whether the new drug causes a decrease in cholesterol for adults with high cholesterol. They recruit a group of adult volunteers with high cholesterol and require each of them to take one pill a day for six months. The volunteers are randomly divided into two groups. One group takes the new drug, while the other group takes an identical salt-water pill with no medicine in it. At the end of six months, they measure the change in cholesterol for all subjects in the sample. They find that the cholesterol level of the adults who took the drug significantly decreased as compared to the cholesterol level of the adults in the other group. The explanatory and response variables in this study are
The explanatory variable - whether a new drug is taken or not The response variable is whether there was a significance decrease in the cholesterol level or not
What type of error represents a false alarm?
Type 1
Suppose that you are considering whether to publish a weekly alternative newspaper on campus. You decide to survey a random sample of students on your campus to ask if they would be likely to read such a newspaper. Your plan is to proceed with publication only if the sample data provides strong evidence that more than 10% of all students on your campus would be likely to read such a newspaper. Describe a Type 2 error.
We don't have evidence the proportion of student readers is more than 10% when it actually is more than 10%. You won't start the newspaper even though you would have had enough readership
As part of a class project, a student conducts a survey of 50 students at her school finding that, thirty-eight of the 50 students (76%) reported owning a smartphone. Is a theory-based confidence interval appropriate for this data?
Yes
A study of human development showed two types of movies to groups of children. Crackers were available in a bowl, and the investigators compared the number of crackers eaten by children watching the different kinds of movies. One kind was shown at 8 A.M. and another at 11 A.M. It was found that during the movie shown at 11 A.M., more crackers were eaten than during the movie shown at 8 A.M. The same type of crackers was used both times and the same bowl was used both times. The investigators concluded that the different types of movies had an effect on appetite. A confounding variable in this experiment is
the time the movie was shown
As part of a class project, a student conducts a survey of 50 students at her school finding that, thirty-eight of the 50 students (76%) reported owning a smartphone. The student conducts a two-sided test of the null hypothesis that the true proportion of students at her school with a smartphone is 50%. This test yields a p-value of <0.001. A 95% confidence interval for the true proportion of all students at the school who own a smartphone
will not contain 50%
o investigate whether giving chest-compression-only (CC) instructions rather than standard cardiopulmonary resuscitation (CPR) instructions to the witness of a heart attack will improve the victim's chance of surviving, researchers Hupfl et al. (The Lancet, 2010) combined the results from three randomized experiments. In each experiment, the emergency services dispatcher randomly assigned either CC or CPR instructions to the bystander who was at the site where a person had just experienced a heart attack. They found that of the 1,500 cases where CC instructions had been given, 211 people had survived, whereas of the 1,531 cases where standard CPR instructions had been given, the number was 178. In this context, which of the following is an appropriate statistic value?
211/1500 - 178/1531 = 0.024
As part of a class project, a student conducts a survey of 50 students at her school finding that, on average, the students in the sample report spending 2.3 hours per day watching TV (SD=2). The student wonders if this is significantly different than the national average of 4.9 hours p/day. The p-value for this test is <0.001. True or False. If the validity conditions are not met, you should use a theory-based method, not a simulation based method of computing a confidence interval
False
Suppose a 95% confidence interval for a population proportion is found using the 2SD or theory-based method. Which of the following will definitely be contained in that interval?
The sample proportion
The confidence level (.90, 95 or .99) indicates the long-run percentage of confidence in the interval that would succeed in capturing the true value of the parameter if random samples were taken repeatedly from the population and a confidence interval were produced from each sample. So, a 95% confidence level means that 95% of the samples would be correct (truly capture the unknown population parameter) and 5% of the samples would be in error.
True
In estimating a population mean, the midpoint of a confidence interval is the observed value of the sample mean (x-bar) and the margin of error increases (widens) when
- the sample size decreases - larger confidence levels are utilized (alpha = 90 to 95 to 99)
The spinning dancer (or silhouette illusion) is a moving image of a woman that appears to be spinning. Some people see her spinning clockwise and some see her spinning counterclockwise. A student showed other students this, and found that 30 out of 50 (or 60%) of them saw her spinning clockwise. The student researcher was interested in the probability of a randomly chosen student that would see the dancer spinning clockwise. He created the following null distribution for this. (a) If the study found that 80% of students saw the dancer spinning clockwise (instead of 60%), how would a 95% confidence interval change?Would it become wider, narrower or remain the same? (b) If the student showed the the spinning dancer to other students 100 times instead of 50 but still found that 30% of them saw her spinning clockwise, how would a 95% confidence interval change? Would it become wider, narrower or remain the same? (c) If we were to compute a 99% confidence interval based on the statistic given in the problem (i.e. 30 out of 50), would it be wider or narrower than 95% confidence interval from part (a) or would it remain the same?
(a) Narrower (b) Narrower (c) wider
A newspaper conducted a statewide survey concerning the 1998 race for governor. The newspaper took a simple random sample of 1200 registered voters and found that 640 would vote for the Democratic candidate.The researchers run a test of significance to see if there is strong evidence that a clear majority of the population would vote for the Democratic candidate? The p-value of the test of significance is .02 and the power of this test was 80%. The researchers used significance level 5%. What is the probability of Type I error?
0.05
The theoretical method requires stipulations or validity conditions because this method relies on formulas which approximate the true null distribution. The randomization does not require these same stipulations or validity conditions and so they do NOT have stipulations.
True
True or False. The purpose of randomization in an experiment is to create treatment groups that 'look alike/have similar characteristics.
True
True or False. You can use the one-sample t-test if your sample has 13 observations and it has a symmetric distribution.
True
A recent study examined hearing loss data for 1771 teenagers. In this sample, 333 were found to have some level of hearing loss.A 95% confidence interval constructed for the parameter of interest in this problem ranges from 0.012 to 0.025.Which of the following statements gives a valid interpretation of this interval?
We are 95% confident that the proportion of all teenagers with some level of hearing loss is between 0.012 and 0.025
As part of a class project, a student conducts a survey of 50 students at her school finding that, thirty-eight of the 50 students (76%) reported owning a smartphone. The student finds a 95% confidence interval to be 64% to 88%. The correct interpretation of this confidence interval is?
We are 95% confident that the true proportion of all students at the school that own smart phone is between 64% and 88%.