Question 1

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

Accepted Answer

An observational study observes characteristics of a sample without intervention, while an experiment involves assigning treatments to study their effects.

Question 2

A researcher wants to know the average number of hours college students spend on community service per month. What is the population in this study?

Accepted Answer

All college students at the researcher's college.

Question 3

Which sampling method ensures that every possible sample of size $$n$$ has an equal chance of being selected?

Accepted Answer

Simple random sampling

Question 4

In a study, researchers found that dog owners had higher heart rate variability than non-owners. Why might exercise be a confounding variable in this study?

Accepted Answer

Dog owners may exercise more, which could affect heart rate variability, making it unclear if the effect is due to dog ownership or exercise.

Question 5

Which of the following is a categorical variable?

Accepted Answer

Political affiliation

Question 6

A histogram is most appropriate for which type of data?

Accepted Answer

Numerical data, especially when the data set is large

Question 7

Given the following data set: 4, 4, 5, 5, 6, 7, 7, 7, 7, 8, 9, 9, 9, 9, 10, 11, 11, 12, 12, 20. What is the interquartile range (IQR)?

Accepted Answer

$$IQR = 10.5 - 6.5 = 4$$

Question 8

Which of the following statements about the mean and median is TRUE for a right-skewed (positively skewed) distribution?

Accepted Answer

The mean is greater than the median.

Question 9

A z-score is calculated as $$z = \frac{x - \bar{x}}{s}. $$What does a z-score of -2.0 mean in a data set?

Accepted Answer

The value is 2 standard deviations below the mean.

Question 10

According to the Empirical Rule, approximately what percentage of data falls within two standard deviations of the mean in a normal distribution?

Accepted Answer

95%

Question 11

Which of the following best describes the coefficient of determination ($$R^2) in $$linear regression?

Accepted Answer

$$R^2 is $$the proportion of variation in $$y$$ explained by the linear relationship with $$x.$$

Question 12

In the context of probability, what is the sample space for tossing a coin twice?

Accepted Answer

$$\{(H, H), (H, T), (T, H), (T, T)\}$$

Question 13

If two events $$A$$ and $$B$$ are independent, which of the following is true?

Accepted Answer

$$P(A|B) = P(A)$$

Question 14

A pie chart is most effective for which type of data?

Accepted Answer

Categorical data with a small number of categories

Question 15

Given the pie chart of fictional characters and their need for life insurance, what is the correct formula to calculate the angle for the 'Batman' slice if the relative frequency is 18%?

Accepted Answer

$$360 	imes 0.18$$

Question 16

Which of the following is NOT a property of Pearson’s correlation coefficient $$r$$?

Accepted Answer

$$r$$ depends on the units of measurement.

Question 17

Suppose you roll a fair die. What is the probability of rolling an odd number or a multiple of 3?

Accepted Answer

$$P(	ext{odd}) + P(	ext{multiple of 3}) - P(	ext{odd} \cap 	ext{multiple of 3}) = \frac{3}{6} + \frac{2}{6} - \frac{1}{6} = \frac{4}{6}$$

Question 18

Which of the following best describes a confounding variable?

Accepted Answer

A variable whose effects on the response variable cannot be distinguished from those of another variable.

Question 19

If the sample mean of a data set is 10 and the sample standard deviation is 2, what is the z-score for a value of 14?

Accepted Answer

$$z = \frac{14 - 10}{2} = 2$$

Question 20

Which of the following is a correct interpretation of the slope in a simple linear regression equation $$y = a + bx$$?

Accepted Answer

The slope $$b is $$the predicted change in $$y$$ for a one-unit increase in $$x.$$

Essential Study Notes for Introductory Statistics: Data Collection, Description, and Probability

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