Statistics Midterm Review

A recent poll by YouGov of 1,600 Americans found 42.0 percent approve of President Biden's handling of the economy. We are almost certain that the percent of Americans who approve of President Biden's handling of the economy is between x percent and y percent. x and y are: 1) 39.5, 44.5 2) 38.3, 43.2 3) 37.0, 47.0 4) 40.5, 43.5

1) 39.5, 44.5

Twenty percent of adults in Columbia, SC have income above $110,000. For adults in the city with income above $110,000, 60 percent have received the flu vaccine. Suppose an adult is selected at random from Columbia, SC, what is the probability the person will have income above $110,000 and have received the flu shot? 1) 0.12 2) 0.10 3) 0.08 4) 0.20

1) 0.12

Suppose you apply to two graduate schools, Harvard and Yale. The probability of getting into Harvard is 0.2 and the probability you get into Yale is 0.3. The probability of getting into both schools is 0.1. What is the probability of getting into Harvard or Yale? 1) 0.40 2) 0.25 3) 0.50 4) 0.60

1) 0.40

Which of the following news story excerpts describes the results of a meta-analysis? 1) A recent analysis of eight international studies found that..." 2) "A recent long-term study using 100,000 participants found that..." 3) "This single study contained 10 parts; each part used a different type of statistical analysis to get the results. The results showed that..." 4) None of the above.

1) 1) A recent analysis of eight international studies found that..."

Suppose you want to survey the opinions of the residents of an apartment complex. The complex contains 100 buildings, each with 8 units per building, for a total of 800 units. Suppose 50 of the buildings (400 total units) are for single individuals, and 50 buildings (400 units) are for families. To get your sample, you randomly select 80 units from single housing and 80 units from family housing. What sampling method did you use? 1) A stratified sample. 2) A systematic sample. 3) A cluster sample. 4) A judgement sample.

1) A stratified sample.

Which of the following is not included in the five-number summary? 1) Mean 2) Median 3) Highest number 4) Lower quartile 5) All of the above are included in the five-number summary.

1) Mean

Which of the following statements is true about random assignment? 1) Random assignment eliminates confounding variables in experiments because each group should be similar, on average, for variables other than the treatment variable. 2) Random assignment ensures the results can be extended to the general population. 3) Random assignment is the same thing as random sampling. 4) None of the above.

1) Random assignment eliminates confounding variables in experiments because each group should be similar, on average, for variables other than the treatment variable.

Regarding Case Study 1.2. "Does Aspirin Prevent Heart Attacks?" Which of the following is true about the study whose results are summarized in Table 1.1 of the textbook: 1) The study finds aspirin prevents heart attacks 2)The study uses a random sample representative of all middle-aged and older adults 3)The study concludes that there is a placebo effect All of the above

1) The study finds aspirin prevents heart attacks

Suppose you want to find out how much money each adult will spend on Valentine's Day this year, on average. Suppose you go to a local mall the day before Valentine's Day and ask the first 50 people you see. What type of sample are you getting here? 1) convenience sample 2) sytematic sample 3) cluster sample 4) self-selected sample

1) convenience sample

To convert a proportion into a percentage you multiply the proportion by ____. {Use one number to fill in the blank.}

100

The total area under the normal curve is equal to 1) The total number of individuals in the population 2) 1 3) Cannot be determined without information on the mean and standard deviation. 4) The total number of individuals in the population with the measurement being studied

2) 1

Suppose your score on the SAT was at the 90th percentile. What does that mean? 1) You got 90% of the questions right. 2) 90% of the other students scored lower than you did. 3) 10% of the other students scored lower than you did 4) None of the above

2) 90% of the other students scored lower than you did.

In a recent study, researchers considered the role of caffeine in pancreatic cancer. They analyzed people recently hospitalized with pancreatic cancer and people recently hospitalized for other reasons. People hospitalized with pancreatic cancer were found to typically drink more coffee than those hospitalized for other reasons. 1) Randomized experiment 2) A case-control study 3) A case study 4) None of the above

2) A case-control study

Suppose you want to survey the opinions of the residents of an apartment complex. The complex contains 100 buildings, each with 8 units per building, for a total of 800 units. Suppose you randomly sample 20 buildings and then interview every person in those 20 buildings. What sampling method did you use? 1) A convenience sample. 2) A cluster sample. 3) A stratified sample. 4) A systematic sample.

2) A cluster sample.

What type of sample would give the most unbiased data? 1) A volunteer sample. 2) A random sample. 3) A sample with a high number of respondents. 4) None of the above.

2) A random sample.

Which of the following describes an experiment with little or no ecological validity? 1) An experiment that is harmful to the environment and can't be justified. 2) An experiment whose variables are measured in an artificial setting and whose results do not accurately reflect the real world. 3) An experiment whose results are not ecologically beneficial. 4) None of the above.

2) An experiment whose variables are measured in an artificial setting and whose results do not accurately reflect the real world.

Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in antinuclear demonstrations. 1) Linda is a bank teller who is active in the feminist movement. 2) Linda is a bank teller.

2) Linda is a bank teller.

Suppose an "Instant Lotto" ticket costs you $5, and the chances of winning the $500 prize are 1/1,000. There are no other prizes. What is your expected value for this game for each ticket you buy? 1) -$4.95 2) $0.05 3) -$4.50 4) $4.95

3) -$4.50

Which of the following would give a news reporter the best and most comprehensive foundation for a news story involving a statistical study? 1) Another newspaper article written by a competitor. 2) A conference presentation given by the researchers themselves. 3) An article in a peer-reviewed scholarly journal, accompanied by a press release. 4) A press release gives everything they need because it's written just for them.

3) An article in a peer-reviewed scholarly journal, accompanied by a press release.

Which statement is not a conclusion of the Empirical Rule? 1) For any normal curve, 68% of the values fall within 1 standard deviation of the mean 2) For any normal curve, 95% of the values fall within 2 standard deviations of the mean 3) For any normal curve, all of the values fall within 3 standard deviations of the mean 4) None of the statements is a conclusion of the Empirical Rule

3) For any normal curve, all of the values fall within 3 standard deviations of the mean

Which of the following is a well-worded survey question for determining a voter's opinion on a tax increase for education? 1) Would you be willing to agree to a small tax increase that would help the education of our children? 2) Do you agree with a tax increase for education? 3) How do you feel about a tax increase for education (agree, disagree, neutral)? 4) All of the above are well-worded questions.

3) How do you feel about a tax increase for education (agree, disagree, neutral)?

Suppose you are conducting an experiment that involves assigning each of 100 participants to one of two groups: Group A or Group B. Which of the following would not be considered to be a random assignment of participants to groups? 1) For each participant, flip a coin. If the coin lands heads up, assign the person to Group A. If the coin lands tails up, assign the person to Group B. 2) Put all 100 names in a hat and mix them up thoroughly. Draw 50 names from the hat and assign them to Group A. Everyone else is assigned to Group B. 3) Recruit study participants on two days (Sunday and Monday). Assign the first 50 who show up on Sunday to Group A, and the first 50 who show up on Monday to Group B. 4) All of the above methods are considered to be random assignments of participants to groups.

3) Recruit study participants on two days (Sunday and Monday). Assign the first 50 who show up on Sunday to Group A, and the first 50 who show up on Monday to Group B.

Which of the following studies would likely be most suitable for a randomized experiment? 1) Studying the effect of male pattern baldness on heart attacks. 2) Studying the effect of smoking on lung cancer. 3) Studying the effect of aspirin use on heart attacks. 4) Studying the effect of smoking by pregnant mothers on the birth weight of babies.

3) Studying the effect of aspirin use on heart attacks.

Which of the following is an example of an open question? 1) "Which of the following four issues do you feel is the most important problem facing this country today? If you prefer, you may name a different problem as most important; simply choose 'other' and explain your answer." (Four choices are given, plus 'other'.) 2) "Don't you think it's time that we faced the fact that unemployment is the biggest problem facing this country today?" (Choices are: yes, no, no opinion.) 3) What do you feel is the most important problem facing this country today?" (No choices offered; participant must fill in the blank.) 4) None of the above.

3) What do you feel is the most important problem facing this country today?

Suppose a health insurance company charges $4,000 a year in premiums. Assume all of their customers will have 1 of 3 outcomes during the year: serious health problems with medical expenses totaling $12,000, moderate health problems with medical expenses totaling $2,000, or no health problems and zero medical expenses. The health insurance company must cover all medical expenses that occur. If the probability a consumer has no health problems is 0.25 and the probability a consumer has serious health problems is 0.1, the expected value of the profit the health insurance company will make on each consumer is: 1) $1,200 2) $2,100 3) -$1,400 4) $1,500

4) $1,500

Suppose your commute to work involves encountering 3 intersections in town and then getting on the Interstate for 10 miles. Your driving experiences in town and on the Interstate are independent. Suppose your chances of hitting a red light in town are 2 in 10, and your chances of getting tied up in traffic on the Interstate are 4 in 10. What are the chances of having both happen on the same trip to work? HINT: Use multiplication rule for independent events. 1) 3/10 = .30 or 30% 2) 2/100 = .02 or 2% 3) 1/25 = .04 or 4% 4) 2/25 = .08 or 8%

4) 2/25 = .08 or 8%

Suppose the five number summary for a variable is: 3, 12, 16, 19, 38. The interquartile range (IQR) is: 1) 35 2) 4 3) 9 4) 7

4) 7

Which of the following describes possible origins of news stories? 1) Academic conferences 2) Scholarly journals 3) Government and private agency reports 4) All of the above

4) All of the above

Which of the following is a property of a confounding variable? 1) It is related to the explanatory variable; individuals who differ on the explanatory variable are also likely to differ on the confounding variable. 2) It affects the response variable. 3) Its effect on the response variable cannot be separated from the effect of the explanatory variable on the response variable. 4) All of the above

4) All of the above

Which of the following is not an example of a common type of research strategy as discussed in your textbook? 1) Sample surveys 2) Randomized experiments 3) Case studies 4) All of the above are examples of common types of research strategies

4) All of the above are examples of common types of research strategies

Which of the following is not true about a standard normal curve? 1) It is symmetric. 2) It has a mean of 0 and standard deviation of 1. 3) Its measurements are Z scores. 4) All of the above are true.

4) All of the above are true.

Which of the following components of a good news report does not pertain to the issue of bias? 1) Knowing the source of the research and of the funding 2) Knowing how the individuals or objects for a study were selected. 3) Knowing the setting in which measurements were taken 4) All of these relate to the issue of bias.

4) All of these relate to the issue of bias.

In the initial vaccine trial by Pfizer for its Covid-19 vaccine, which of the following is not true: 1) A placebo vaccine shot of saline solution was given to members of the control group 2) Individuals were assigned to treatment and control groups based on randomization 3) The vaccine was found to be 95 % effective 4) Individuals in the treatment group were told they were receiving the actual vaccine

4) Individuals in the treatment group were told they were receiving the actual vaccine

Which statement about personal probabilities is true? 1) They are subjective 2) They can be informed by data 3) They do not have to be between 0 and 1 4) The first two answers are true about personal probabilities, but not the third answer

4) The first two answers are true about personal probabilities, but not the third answer

If 1,000 surveys go out and 400 of them are returned, the response rate is __________ percent. {Use a number to fill in the blank.}

40

A(n) __________ variable is one that attempts to explain or is purported to cause (at least partially) differences in a response variable.

Explanatory

In a survey, the wording but not the ordering of the questions can influence answers (T/F)

False

Observational studies are as good as randomized experiments for purposes of determining causal connections. (T/F)

False

Random assignment in experiments ensures any relationships that are found can be generalized to the general population. HINT: Think about the experimental study of aspirin and heart attacks among a sample of physicians. (T/F)

False

Suppose researchers examined the relationship between breakfast eating habits (explanatory variable) and obesity (response variable) in school kids from low-income families. The researchers randomly assigned children to different diets, with some children being given cereal every day during the experiment and some children being given breakfast items other than cereal. Researchers found the group with the cereal diet had lower body mass indices (BMIs) at the end of the experiment than children with the non-cereal diet. (T/F)

False

Suppose the height of women in the U.S. has a normal distribution. A woman's height that was more than 3 standard deviations above or below the mean height for women would not be an extreme outlier. (T/F)

False

An observational study that follows a group of high school students into the future, recording how many children they have (if any) and at what age(s) they had those children is an example of a(n) __________ study.

Prospective

A Pareto chart helps to separate the "vital few" categories from the "trivial" many. (T/F)

True

Highest level of education completed (grade school, high school, college, higher than college) is an ordinal variable. (T/F)

True

If P(A|B)=P(A), then the events A and B are independent. (T/F)

True

If you are told that your Z-score on an exam is 1.5, it means that your score is 1.5 standard deviations above the mean. (T/F)

True

Random assignment ensures any relationships that are found in the data are causal in nature (T/F)

True

Suppose researchers examined the relationship between breakfast eating habits (explanatory variable) and obesity (response variable) in school kids from low-income families. Researchers observed the body mass indices (BMIs) of 625 children and recorded the number of times, out of 9 days, that children said they ate breakfast. Kids who reported eating breakfast 4 out of 9 days tended to be in the 95th percentile for BMIs, indicating obesity. Kids who reported eating breakfast 9 out of 9 days tended to be in the 65th percentile, indicating healthy weights. (T/F)

True

The number of people in a population would be denoted by N and the number of people in a sample would be denoted by n. (T/F)

True

The standard deviation is roughly the average distance of the observed values from their mean. (T/F)

True

The population is the entire group for which you plan to draw conclusions. The __________ is the group that is actually studied, and is chosen from the population. (Use one word to fill in the blank.)

sample

Suppose you conduct an observational study as follows: you survey 200 people who had been on a weight loss program for six months, and ask them whether or not they take vitamins every day, and how much weight they lost. Suppose you found that the people who lost the most weight were more likely to have taken vitamins every day.

true