Question 1

Which of the following best describes the difference between a population and a sample in statistics?

Accepted Answer

A population includes all individuals of interest, while a sample is a subset selected from the population.

Question 2

A researcher wants to compare the average test scores of students in two different schools. Which of the following best describes the type of variable 'school'?

Accepted Answer

Categorical variable

Question 3

Which of the following graphs is most appropriate for displaying the distribution of a single categorical variable?

Accepted Answer

Bar chart

Question 4

Suppose the heights (in cm) of a group of students are normally distributed with mean $$\mu = 170$$ and standard deviation $$\sigma = 10. $$According to the empirical rule, approximately what percentage of students have heights between 160 cm and 180 cm?

Accepted Answer

$$68\%$$

Question 5

A data set of exam scores has a mean of $$75$$ and a standard deviation of $$5. A $$student scored $$85 on $$the exam. What is the student's $$z-$$score?

Accepted Answer

$$z = 2$$

Question 6

Which of the following statements about the correlation coefficient $$r is $$FALSE?

Accepted Answer

$$r$$ can be used to infer causation between two variables.

Question 7

A boxplot is constructed for the following data set: $$\{6, 8, 10, 12, 14, 16, 18, 20, 27\}. $$What is the interquartile range (IQR)?

Accepted Answer

$$IQR = 10$$

Question 8

Which of the following is NOT a measure of central tendency?

Accepted Answer

Interquartile range (IQR)

Question 9

A researcher collects data on the number of hours students study and their exam scores. Which type of graph should be used to display the relationship between these two variables?

Accepted Answer

Scatterplot

Question 10

Suppose a linear transformation is applied to a data set: $$y = 3x + 2. If $$the original mean is $$\bar{x} = 5$$ and the original standard deviation is $$s_x = 4$$, what are the mean and standard deviation of $$y$$?

Accepted Answer

Mean $$= 17$$, Standard deviation $$= 12$$

Question 11

Which of the following best describes Simpson's paradox?

Accepted Answer

A trend appears in different groups of data but disappears or reverses when the groups are combined.

Question 12

A contingency table is used to:

Accepted Answer

Summarize the relationship between two categorical variables.

Question 13

Which of the following is an example of a double-blind study?

Accepted Answer

Neither the participants nor the researchers know which group receives the treatment.

Question 14

A sample of weights (in kg) is: $$\{60, 65, 70, 75, 80\}. $$What is the sample mean?

Accepted Answer

$$70$$

Question 15

Which of the following statements about outliers is TRUE?

Accepted Answer

Outliers can have a large effect on the mean and standard deviation.

Question 16

In a regression analysis, the coefficient of determination $$R^2$$ represents:

Accepted Answer

The proportion of the variance in the response variable explained by the explanatory variable.

Question 17

Which of the following is a potential source of bias in survey sampling?

Accepted Answer

Non-response bias

Question 18

A histogram is most appropriate for which type of data?

Accepted Answer

Quantitative data

Question 19

If a data set is skewed to the right, which of the following is most likely true?

Accepted Answer

Mean $$\u003e$$ Median

Question 20

Which of the following best describes the purpose of randomization in experimental studies?

Accepted Answer

To reduce the impact of confounding variables and bias

Basic Statistics and Data Science: Exam Study Guide and Practice Questions

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