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89Good job! We need to find the exam score such that the probability of getting a score above it is 0.04. Equivalently (and more practical, given the way our table works) we need to find the exam score such that the probability of getting a score below it is 1 – 0.04 = 0.96. Looking in the body of t...
Read MoreColor-blindness is any abnormality of the color vision system that causes a person to see colors differently than most people or to have difficulty distinguishing among certain colors (www.visionrx.xom).
Color-blindness is gender-based, with the majority of sufferers being males.
Roughly 8% of white males have some form of color-blindness, while the incidence among white females is only 1%.
A random sample of 20 white males and 40 white females was chosen.
Let X be the number of males (out of the 20) who are color-blind.
Let Y be the number of females (out of the 40) who are color-blind.
Let Z be the total number of color-blind individuals in the sample (males and females together).
Which of the following is true regarding the random variables X and Y?
Neither X nor Y can be well-approximated by a normal random variable....
Read MoreWhat is the mean and standard deviation of the random variable Y (the number of females out of 40 who are veg friendly)? Answers may be rounded.
Good job! Indeed the mean and standard deviation of a binomial random variable are np and
Mean: 15.6Standard Deviation: 3.08Good job! Indeed the mean and standard deviation of a binomial random variable are np and...
Read MoreWhat is the probability that exactly 2 of the 20 males are veg-friendly? (Note: Some answers are rounded.)
.078Good job! We need to find P(X = 2) where X is binomial with n = 20 and p = 0.24:...
Read MoreA restaurant chain wants to create dishes that will attract new clientele. They are interested in adding some vegetarian and vegan options to their menu. A survey revealed that 24% of males and 39% of females order vegetarian while out.
60 clients were randomly selected: 20 men and 40 women.
Let X be the number of males (out of 20) who order vegetarian sometimes.
Let Y be the number of females (out of 40) who order vegetarian sometimes.
Let Z be the total number in the sample who order vegetarian sometimes (out of 60).
All of the above are trueGood job! X represents the number of veg-friendly males out of a random sample of 20 → X is binomial with n = 20 and p = 0.24. Y represents the number of veg-friendly females out of a random sample of 40 → Y is also binomial with n = 40 and p = 0.39. Z represents the total n...
Read MoreA parking garage has two entrances. Let X be the number of cars that enter the garage through door A in an hour, and Y be the number of cars that enter through door B in an hour. Assuming that μx = 15 and μy = 25, what is the mean of Z, the total number of cars that enter the garage in an hour.
40...
Read MoreThe number of people in a car that crosses a certain bridge is represented by the random variable X, which has a mean value μX = 2.7, and a variance σ2X = 1.2. The toll on the bridge is $3.00 per car plus $ .50 per person in the car. The mean and variance of the total amount of money that is collected from a car that crosses the bridge are:
mean = $4.35, variance = $ .30.Good job! Let T be the total amount of money that is collected from a car that crosses the bridge. T is composed of two parts: the fixed toll of 3 dollars (regardless of the number of passengers) and $ .50 for every passenger, thus T = 3 + 0.50 * X. To fin...
Read MoreFor their 1992 study “The Effect of Country Music on Suicide” (published in Social Forces, vol. 71, p. 211), researchers Stack and Gundlach investigated various American communities, recording the number of minutes of daily radio airtime devoted to country songs and the suicide rate. They found a moderately strong positive correlation.
In their paper, the researchers explain the results by saying that “…the themes found in country music foster a suicidal mood ...” (emphasis added). A news headline (The Independent [London], October 1, 2004, p. 15) about the research echoed these sentiments when it said, “Strange But True: Country Music Saps Will to Live.” The research is even cited on various suicide-prevention websites, some with headings such as “Country Music Increases Suicide Risk.”
Based upon this study, can we have confidence that country music has a causal effect on suicide?
Good job! Causation can only be determined if the explanatory variable is randomly assigned. But in this case, the researchers didn't randomly assign different amounts of country music to be played in different communities. So the study design doesn't rule out lurking variables.
No, because the lack of assignment of communities to different levels of country music listening means there is a possibility of lurking variables.Causation can only be determined if the explanatory variable is randomly assigned. But in this case, the researchers didn't randomly assign dif...
Read MoreTo test an herbal treatment for headaches, 100 volunteers who suffered from mild headaches were randomly divided into two groups. Each person was given a month's supply of tea bags. For one group, the tea contained the herb mixed with green tea, whereas for the other group, the bags contained only the green tea. Participants were not told which type of tea they had, and were asked to drink one cup of tea per day for a month.
At the end of the month, a researcher evaluated them to determine if the length and number of headaches had improved. The researcher did not know which of the subjects had the tea with the herbal ingredient added.
Which is true regarding this study?
Only (A) and (B) are true.The study is double-blind, because the subjects didn’t know which tea they got (which protects against the placebo effect), and the researcher also didn’t know (which helps guard against researcher bias). In addition, the "only green tea" group serves as the control group b...
Read MoreStudents in a large statistics class were randomly divided into two groups. The first group took the midterm exam with soft music playing in the background while the second group took the exam with no music playing. The exam scores of the two groups were then compared.
This experiment was not blind because:
the students knew whether or not music was playing while they were taking the exam.Good job! "Blinding" in study design is when the subjects don’t know which treatment they’re getting. In this case, the treatments are background music or no background music. The students would certainly be aware of ...
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The remaining questions refer to the following information:
Suppose the scores on an exam are normally distributed with a mean μ = 75 points, and standard deviation σ = 8 points.