Question 1

Which of the following best describes the difference between a parameter and a statistic?

Accepted Answer

A parameter is a numerical summary of a population, while a statistic is a numerical summary of a sample.

Question 2

A researcher wants to study the average cholesterol level among adults in a city. She divides the city into neighborhoods and randomly selects several neighborhoods, then surveys all adults in those neighborhoods. Which sampling method is she using?

Accepted Answer

Cluster sampling

Question 3

Which of the following variables is best classified as continuous numerical?

Accepted Answer

Temperature measured in degrees Celsius

Question 4

A frequency table shows the number of students who scored in different ranges on a test. If 10 students scored between 80 and 89, and the total number of students is 50, what is the relative frequency for the 80–89 range?

Accepted Answer

$$0.2$$

Question 5

Which graphical display is most appropriate for showing the distribution of a categorical variable such as 'favorite ice cream flavor'?

Accepted Answer

Pie chart

Question 6

Given the data set: $$2, 4, 4, 6, 8$$, what is the interquartile range (IQR)?

Accepted Answer

$$2$$

Question 7

A boxplot is useful for visualizing which of the following?

Accepted Answer

The distribution and spread of a numerical variable, including outliers

Question 8

If the mean of a data set is $$50$$ and the standard deviation is $$5$$, what is the variance?

Accepted Answer

$$25$$

Question 9

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

Accepted Answer

$$r$$ measures the strength and direction of a linear relationship between two variables

Question 10

A scatter diagram shows a strong positive linear relationship between hours studied and exam score. Which value is most likely for the correlation coefficient $$r$$?

Accepted Answer

$$0.90$$

Question 11

In a regression analysis, the equation of the least squares regression line is $$y = 3x + 2. $$What does the slope $$3$$ represent?

Accepted Answer

For every unit increase in $$x$$, $$y$$ increases by $$3$$ units.

Question 12

A student uses the regression equation $$y = 2x + 5 to $$predict $$y$$ for $$x = 20$$, but the data only included $$x$$ values between $$1$$ and $$10. $$What is the main concern with this prediction?

Accepted Answer

The prediction may be unreliable due to extrapolation beyond the observed range.

Question 13

If the coefficient of determination $$R^2$$ for a regression model is $$0.81$$, what does this mean?

Accepted Answer

81% of the variation in the response variable is explained by the model.

Question 14

Which of the following best describes a residual in regression analysis?

Accepted Answer

The difference between the observed value and the predicted value.

Question 15

A residual plot shows a random scatter of points around zero. What does this indicate about the linearity assumption?

Accepted Answer

The linearity assumption is likely satisfied.

Question 16

A medical study randomly assigns patients to receive either a new drug or a placebo and compares their recovery rates. What type of study is this?

Accepted Answer

Experimental study

Question 17

Which sampling method involves selecting every $$kth $$individual from a list after a random start?

Accepted Answer

Systematic sampling

Question 18

If a data set has a mean of $$60$$, median of $$55$$, and mode of $$50$$, what can you infer about the shape of the distribution?

Accepted Answer

The distribution is skewed to the right.

Question 19

A side-by-side boxplot is most useful for:

Accepted Answer

Comparing the distribution of a numerical variable across different groups.

Introductory Statistics Midterm Study Guide: Chapters 1–4

Study Guide - Practice Questions

Study Guide - Flashcards