Question 1

Which of the following best describes the difference between an observational study and an experiment?

Accepted Answer

An observational study observes subjects without intervention, while an experiment involves applying treatments to measure effects.

Question 2

A pharmaceutical company wants to test a new drug. They randomly assign patients to receive either the drug or a placebo, and neither the patients nor the doctors know which treatment is given. What type of experimental design is this?

Accepted Answer

Double-blind experiment

Question 3

Which sampling method divides the population into subgroups and then randomly selects members from each subgroup?

Accepted Answer

Stratified sample

Question 4

Given the following data set representing the number of hours students studied for an exam: 2, 4, 4, 6, 8, 10. What is the median?

Accepted Answer

$$5$$

Question 5

A teacher records the test scores of her class: 70, 75, 80, 85, 90. What is the mean score?

Accepted Answer

$$80$$

Question 6

Which formula is used to calculate the sample standard deviation $$s$$ for a data set $$x_1$$, $$x_2$$, ..., x_n$$ with mean $$\overline{x}$$?

Accepted Answer

$$s = \sqrt{\frac{\sum_{i=1}^{n} (x_i - \overline{x})^2$}{n-1}}$$

Question 7

A data set has a mean of $$50$$ and a standard deviation of $$5. $$According to the Empirical Rule, approximately what percentage of data falls between $$40$$ and $$60$$?

Accepted Answer

$$68\%$$

Question 8

Which measure of central tendency is most affected by extreme values (outliers)?

Accepted Answer

Mean

Question 9

A researcher wants to summarize the spread of a data set. Which statistic should they use to describe the range between the first and third quartiles?

Accepted Answer

Interquartile Range (IQR)

Question 10

Chebyshev's inequality states that for any data set, at least what proportion of values lie within $$k$$ standard deviations of the mean?

Accepted Answer

$$1 - \frac{1}{k^2$}$$

Question 11

A hospital wants to compare the average recovery time for two treatments. Which type of variable is 'recovery time'?

Accepted Answer

Continuous quantitative

Question 12

Which of the following best describes a frequency polygon?

Accepted Answer

A line graph that connects midpoints of class intervals at their frequencies

Question 13

A survey asks respondents to rate their satisfaction on a scale from 1 to 5. What type of data is this?

Accepted Answer

Ordinal

Question 14

Which of the following is NOT a characteristic of a simple random sample?

Accepted Answer

Members are selected based on convenience

Question 15

A scatterplot shows a strong positive linear relationship between two variables. Which value of the correlation coefficient $$r is $$most likely?

Accepted Answer

$$r = 0.90$$

Question 16

Given the regression equation $$\hat{y} = 2 + 3x$$, what is the predicted value of $$y$$ when $$x = 4$$?

Accepted Answer

$$14$$

Question 17

Which of the following is a potential misleading deceptive graph technique?

Accepted Answer

Starting the y-axis at a value other than zero to exaggerate differences

Question 18

A researcher calculates the five-number summary for a data set. Which values are included?

Accepted Answer

Minimum, first quartile, median, third quartile, maximum

Question 19

A study finds a correlation coefficient $$r = 0.05$$ between hours studied and exam score. What does this indicate?

Accepted Answer

There is little to no linear relationship

Question 20

A dataset has the following five-number summary: $$10, 20, 30, 40, 50. $$What is the interquartile range (IQR)?

Accepted Answer

$$20$$

Statistics Study Guide: Key Concepts, Data Presentation, and Regression Analysis

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