Question

An AP® Statistics student designs an experiment to see whether today’s high school students are becoming too calculator-dependent. She prepares two quizzes, both of which contain 40 questions that are best done using paper-and-pencil methods. A random sample of 30 students participates in the experiment. Each student takes both quizzes—one with a calculator and one without—in random order. To analyze the data, the student constructs a scatterplot that displays a linear association between the number of correct answers with and without a calculator for the 30 students. A least-squares

regression yields the equation. calculator^ = −1.2 + 0.865 (pencil) r = 0.79

Which of the following statements is/are true?

I. If the student had used Calculator as the explanatory variable, the correlation would remain the same.

II. If the student had used Calculator as the explanatory variable, the slope of the least-squares line would remain the same.

III. The standard deviation of the number of correct answers on the paper-and-pencil quizzes was smaller than the standard deviation on the calculator quizzes.

a. I only

b. II only

c. III only

d. I and III only

e. I, II, and III

Short answer

The correct option is (e) I, II, and III

Step-by-step solution

Given information

$$\begin{gathered} \stackrel{⏜}{calculator}=-1.2+0.865\left(pencil\right) \\ r=0.79 \end{gathered}$$

Explanation

We must determine which of the following conclusions is the most appropriate. Thus, all of the options except (e) are incorrect because the statements show that there is no, negative, or positive relationship between the variables. However, option (e) makes a good point, stating that we should examine the scatterplot to see if the variables appear to have a curved relationship. As a result, option (e) is the proper choice.