Updated: Introduction to Probability and Data with R Quiz Answers

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Week 01 Practice Quiz

Q1. Which of the following classifications of variable types is false?

Answer: The population of each state in the US → Continuous numerical

Q2. True or False: If subjects are randomly assigned to treatments, conclusions can be generalized to the population.

Answer: True

Q3. As part of a statistics project, Andrea would like to collect data on household size in her city. To do so, she asks each person in her statistics class for the size of their household and reports that her sample is a simple random sample. However, this is not a simple random sample. Which of the following is the best reasoning for why this is not a random sample that is appropriate for this research question?

Answer: Andrea did not use any randomization; she took a convenience sample.

Q4. Which of the following is not one of the four principles of experimental design?

Answer: stratify

Q5. True or False: Stratified sampling allows for controlling for possible confounders in the sampling stage while blocking allows for controlling for such variables during the random assignment.

Answer: True

Introduction to Probability and Data with R Week 01 Quiz Answers

Q1. Consider the table below describing a data set of individuals who have registered to volunteer at a public school. Which of the choices below lists categorical variables?

• name and number of siblings
• number of siblings and year born
• annual income and phone number
• phone number and name

Q2. A study is designed to test the effect of type of light on exam performance of students. 180 students are randomly assigned to three classrooms: one that is dimly lit, another with yellow lighting, and a third with white fluorescent lighting, and given the same exam. Which of the following correctly identifies the variables used in the study as explanatory and response?

• explanatory: exam performance

response: type of light (categorical with 3 levels)

• explanatory: exam performance

response: dimly lit, yellow, white fluorescent

• explanatory: dimly lit, yellow, white fluorescent

response: exam performance

• explanatory: type of light (categorical with 3 levels)

response: exam performance

Q3. Past research suggests that students who study with fewer distractions (internet, cell phone, etc.) tend to get higher grades. Which of the following is the best scenario for being able to generalize this finding to the population of all students?

• The students participate in the study after seeing signs about the survey posted around campus.
• Sample only includes students who are in classes that the researcher teaches.
• A survey is emailed to all registered students, and the results are based on the sample of returned surveys.
• A student list for the college is obtained and students are randomly selected from the list, and all selected students participate in the study.

Q4. An extraneous variable that is related to the explanatory and response variables and that prevents us from deducing causal relationships based on observational studies is called a _______ (use all lower cases in your answer please).

Answer: confounding variable

Q5. For your political science class, you’d like to take a survey from a sample of all the Catholic Church members in your town. Your town is divided into 17 neighborhoods, each with similar socio-economic status distribution and ethnic diversity, and each contains a Catholic Church. Rather than trying to obtain a list of all members of all these churches, you decide to pick 3 churches at random. For these churches, you’ll ask to get a list of all current members and contact 100 members at random. What kind of design have you used?

• stratified sampling
• simple random sampling
• systematic sampling
• quota sampling
• multistage sampling

Q6. Which of the following is not one of the four principles of experimental design?

• block
• cluster
• replicate
• control

Q7. Which of the following is one of the four principles of experimental design?

• control
• cluster
• stratify

Introduction to Probability and Data with R Week 02 Quiz Answers

Q1. Which of the below data sets has the highest standard deviation? You do not need to calculate the exact standard deviations to answer this question.

Answer: 0,1,1,1,1,1,2

Q2. The distribution of housing prices in a country where 25% of the houses cost below $350,000, 50% of the houses cost below $450,000, 75% of the houses cost below $1,000,000 and there are a meaningful number of houses that cost more than $6,000,000 is most likely

• symmetric
• left skewed
• right skewed
• uniform

Q3. Based on the relative frequency histogram below, which of the following statements is supported by the plot?

• The mean of the distribution is smaller than its median.
• There are no outliers in the distribution.
• It is not possible to estimate the median without knowing the sample size.
• The IQR of the distribution is roughly 10.
• The distribution is multimodal.

Q4. Which is more affected by extreme observations, the mean or median? And how about the standard deviation or IQR?

• mean, SD
• median, IQR
• mean, IQR
• median, SD

Q5. It is relatively common for fish to be mislabeled in supermarkets and even in restaurants. The table below shows the results of a study where a random sample of 156 fish for sale were collected and genetically tested. The researchers classified each sample as being labeled properly or being mislabeled. What fraction of smoked fish in the sample were mislabeled? Choose the closest answer.

• 78%
• 9%
• 28%
• 72%
• 18%

Q6. In 1948, Austin Bradford Hill, designed a study to test a new treatment for tuberculosis that at the beginning of the study there was no evidence whether it would be any better or worse than bed rest. He randomly assigned some patients who volunteered to be a part of this study to receive the treatment Streptomycin, an antibiotic. The other patients received only bed rest as the control group. Hill then observed the patients’ outcomes: which patients died and which recovered. The results of the study are shown below.

We use the following simulation test if there is a difference between the recovery rates under the two treatments: We write “died” on 18 index cards and “survived” on 89 index cards to indicate whether or not a patient died. Next, we shuffle the cards and deal them into two groups of 52 and 55, for control and treatment, respectively. We then calculate the simulated difference between the recovery rates in Streptomycin and control groups (p̂Streptomycin − p̂Control), and record this value. We repeat this simulation 100 times. The histogram below shows the distribution simulated difference between the recovery rates in these 100 simulations.

Which of the following is correct? Choose all that apply (there are multiple correct answers).

• Hill’s study is observational.
• Based on this study we can conclude a causal relationship between Streptomycin and better tuberculosis recovery rate.
• If Streptomycin and bed rest are equally effective in curing tuberculosis, the probability of observing a difference in the recovery rates at least as high as the one observed is 2%.
• Streptomycin treatment does not appear to be effective in treating tuberculosis since the observed number of deaths in the treatment group would not be considered unusual based on the simulation results.
• The difference between the survival rates in the control and treatment groups appear to be simply due to chance.
• The alternative hypothesis is that the Streptomycin treatment is more effective than bed rest.
• The alternative hypothesis should be that there is a difference between the recovery rates under the two treatments.
• The conclusion of this study is generalizable to all tuberculosis patients.
• Streptomycin treatment appears to be effective in treating tuberculosis since the observed difference in recovery rates would be considered unusual based on the simulation results.

Introduction to Probability and Data with R Week 03 Quiz Answers

Q1. Which of the following states that the proportion of occurrences with a particular outcome converges to the probability of that outcome?

Answer: Law of large numbers

Q2. Each choice below shows a suggested probability distribution for the method of access to online course materials (desktop computer, laptop computer, tablet, smartphone). Determine which is a proper probability distribution.

• desktop computer: 0.25, laptop computer: 0.35, tablet: 0.15, smartphone: 0.25
• desktop computer: 0.15, laptop computer: 0.50, tablet: 0.30, smartphone: 0.20
• desktop computer: 0.20, laptop computer: 0.20, tablet: 0.20, smartphone: 0.20
• desktop computer: 0.30, laptop computer: 0.40, tablet: 0.35, smartphone: -0.05

Q3. Assortative mating is a nonrandom mating pattern where individuals with similar genotypes and/or phenotypes mate with one another more frequently than what would be expected under a random mating pattern. Researchers studying this topic collected data on eye colors of 204 Scandinavian men and their female partners. The table below summarizes the results. For simplicity, assume heterosexual relationships. What is the probability that a randomly chosen male respondent with blue eyes has a partner with blue eyes?

(Reference: Laeng, Bruno, Ronny Mathisen, and Jan-Are Johnsen. “Why do blue-eyed men prefer women with the same eye color?.” Behavioral Ecology and Sociobiology 61.3 (2007): 371-384.)

• 78/108
• (108+114−78)/204
• 78/204
• 78/114

Q4. Which of the following is false?

• When computing the probability that a card drawn randomly from a standard deck is either a Jack or a 4, you can use the addition rule.
• If two outcomes of a random process (both with probability greater than 0) are mutually exclusive, they are not necessarily complements.
• If two events (both with probability greater than 0) are mutually exclusive, they could be independent.
• If the probabilities of two mutually exclusive outcomes of a random process add up to 1, they are complements.

Introduction to Probability and Data with R Week 04 Quiz Answers

Q1. Suppose that scores on a national entrance exam are normally distributed with a mean 1000 and a standard deviation of 100. Which of the following is false?

Answer: We would expect the number of people scoring above 1200 to be more than the number of people scoring below 900

Q2. A 2005 survey found that 7% of teenagers (ages 13 to 17) suffer from an extreme fear of spiders (arachnophobia). At a summer camp, there are 10 teenagers sleeping in each tent. Assume that these 10 teenagers are independent of each other. What is the probability that at least one of them suffers from arachnophobia?

Answer: 62%

Q3. Your roommate loves to eat Chinese food for dinner. He estimates that on any given night, there’s a 30% chance he’ll choose to eat Chinese food. Although he loves Chinese food, he doesn’t like to eat it too much in a short period of time, so on most weeks he eats several different kinds of foods for dinner. Suppose you wanted to calculate the probability that, over the next 7 days, you friend eats Chinese food at least 3 times. Which of the following is the most accurate statement about calculating this probability?

Answer: Because he doesn’t like to eat Chinese food too much in a short period of time, p is not really the same for each trial and so we cannot use the binomial distribution to calculate the desired probability.

Q4. Which of the following, on its own, is the least useful method for assessing if the data follow a normal distribution?

Answer: Check if the mean and median are equal

Q5. Which of the following is true? Hint: It might be useful to sketch the distributions.

Answer: The Z score for the median is approximately 0 if the distribution is bimodal and symmetric

Q6. At any given time about 5.5% of women (age 15-45) are pregnant. A home pregnancy test is accurate 99% of the time if the woman taking the test is actually pregnant and 99.5% accurate if the woman is not pregnant. If the test yields a positive result, what is the posterior probability of the hypothesis that the woman is pregnant?

• 0.995
• 0.99
• 0.08
• 0.92

Q7. One strange phenomenon that sometimes occurs at U.S. airport security gates is that an otherwise law-abiding passenger is caught with a gun in his/her carry-on bag. Usually the passenger claims he/she forgot to remove the handgun from a rarely-used bag before packing it for airline travel. It’s estimated that every day 3,000,000 gun owners fly on domestic U.S. flights. Suppose the probability a gun owner will mistakenly take a gun to the airport is 0.00001. What is the probability that tomorrow more than 35 domestic passengers will accidentally get caught with a gun at the airport? Choose the closest answer.

• 0.91
• 0.02
• 0.18
• 0.82
• 0.28

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