Q: In the mtcars dataset, the weights (in 1000 lbs) of the automobiles are analyzed. If the interquartile range (IQR) is used to detect outliers, which formula is correct for identifying outliers?

$$Q_1 - 1.5$$ \times IQR$$ and Q_3$ + 1.5 \times IQR$$

Question 1

A public health researcher wants to study healthcare providers in rural areas across five states. She randomly selects 8 counties from the 100 total counties, and then surveys all healthcare providers within those 8 selected counties. Which sampling method is being used?

Accepted Answer

Cluster sampling

Question 2

A quality control manager has a production line with 1,000 items produced daily. To inspect the products, she divides 1,000 by the desired sample size of 50, getting an interval of 20. She randomly picks a starting point of 8, then inspects items 8, 28, 48, 68, and so on. Which sampling method is being used?

Accepted Answer

Systematic sampling

Question 3

A university researcher wants to study academic performance across all class years. The population of 2,000 students consists of 500 freshmen, 600 sophomores, 500 juniors, and 400 seniors. The researcher randomly selects 50 freshmen, 60 sophomores, 50 juniors, and 40 seniors to maintain proportional representation. Which sampling method is being used?

Accepted Answer

Stratified sampling

Question 4

An education researcher randomly selects 250 teachers from all public school teachers across a state to assess professional development needs. What is the population in this scenario?

Accepted Answer

All public school teachers in the state

Question 5

A real estate analyst is studying properties in a metropolitan area and collects data on property price, square footage, number of bedrooms, and zipcode. Which of these variables is qualitative?

Accepted Answer

Zipcode

Question 6

Researchers recruit 2,000 adults without heart disease and classify them as either regular exercisers or sedentary individuals based on their baseline activity levels. They then follow both groups prospectively for 15 years, documenting which individuals develop heart disease during the follow-up period. Which study design is being used?

Accepted Answer

Cohort study

Question 7

Researchers are investigating the relationship between prolonged computer use and carpal tunnel syndrome. They identify 150 employees who have been diagnosed with carpal tunnel syndrome and 150 matched employees without the condition. Both groups are then asked detailed questions about their computer usage patterns over the past 10 years. Which study design is being used?

Accepted Answer

Case-control study

Question 8

A researcher is conducting a clinical trial to test the effectiveness of a new medication for hypertension. The study involves patients of varying ages, genders, and baseline health conditions. The researcher wants to ensure that differences in patient characteristics do not confound the treatment effects. Which experimental design would be most appropriate?

Accepted Answer

Randomized Block Design

Question 9

A botanist is testing the effect of four different fertilizer types on plant growth. The experiment will be conducted in a greenhouse where temperature, humidity, and light are all precisely controlled. The researcher has a large number of genetically identical plant seedlings. What is the best experimental design for this study?

Accepted Answer

Completely Randomized Design

Question 10

A marketing research firm wants to determine the most effective method of advertising: print, radio, television, or online. They recruit 4800 volunteers and segment them by their highest degree. Volunteers from each group are randomly assigned to one of the four advertising groups. After exposure, a recall exam is given. What is the response variable?

Accepted Answer

The score on the recall exam

Question 11

In a double-blind experiment, why is it necessary for both the subjects and the individuals monitoring the subjects to be unaware of who receives the treatment and who receives the placebo?

Accepted Answer

So that the subjects receiving the medication do not behave differently and so the individual monitoring the subjects does not treat those receiving medication differently from those receiving a placebo.

Question 12

The histogram below displays the distribution of the exam grades of a statistics class. What percentage of students got an A in the exam (i.e., scored 90 or above)? (Refer to the histogram provided.)

Accepted Answer

$$16\%$$

Question 13

A stem-and-leaf plot of quiz grades is given. The class average is calculated as $$37.625. $$Which of the following best describes how to compute the mean from a stem-and-leaf plot?

Accepted Answer

Add all the values and divide by the number of values.

Question 14

The boxplot shows that the distribution of the dataset is skewed to the right. What does this indicate about the data?

Accepted Answer

The mean is greater than the median.

Question 15

A chemistry test has a maximum of 100 points. The class average is 75 and the standard deviation is 5. Toby scored 80. What is Toby's z-score?

Accepted Answer

$$z = 1$$

Question 16

A calculus test has a maximum of 150 points. The class average is 100 and the standard deviation is 10. Toby scored 120. What is Toby's z-score?

Accepted Answer

$$z = 2$$

Question 17

Given Toby's z-scores for chemistry ($$z = 1) $$and calculus ($$z = 2$$), which score is better relative to the class?

Accepted Answer

The calculus score is better.

Question 18

A dataset contains information about 777 U.S. colleges and universities. The variable 'Enroll' records the number of new students in each school. If the average number of new students is 780, what is the correct interpretation of this value?

Accepted Answer

It is the mean number of new students.

Question 19

In the mtcars dataset, the weights (in 1000 lbs) of the automobiles are analyzed. If the interquartile range (IQR) is used to detect outliers, which formula is correct for identifying outliers?

Accepted Answer

$$Q_1 - 1.5$$ 	imes IQR$$ and Q_3$ + 1.5 	imes IQR$$

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