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Section I: Multiple Choice Choose the best answer for Questions AP1.1 to AP1.14. Before

Chapter 4, Problem AP1.9

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QUESTION:

Section I: Multiple Choice Choose the best answer for Questions AP1.1 to AP1.14.

Before he goes to bed each night, Mr. Kleen pours dishwasher powder into his dishwasher and turns it on. Each morning, Mrs. Kleen weighs the box of dishwasher powder. From an examination of the data, she concludes that Mr. Kleen dispenses a rather consistent amount of powder each night. Which of the following statements is true?

I. There is a high positive correlation between the number of days that have passed since the box of dishwasher powder was opened and the amount of powder left in the box.

II. A scatterplot with days since purchase as the explanatory variable and amount of dishwasher powder used as the response variable would display a strong positive association.

III. The correlation between the amount of powder left in the box and the amount of powder used should be −1.

(a) I only         (d) II and III only

(b) II only         (e) I, II, and III

(c) III only

Questions & Answers

QUESTION:

Section I: Multiple Choice Choose the best answer for Questions AP1.1 to AP1.14.

Before he goes to bed each night, Mr. Kleen pours dishwasher powder into his dishwasher and turns it on. Each morning, Mrs. Kleen weighs the box of dishwasher powder. From an examination of the data, she concludes that Mr. Kleen dispenses a rather consistent amount of powder each night. Which of the following statements is true?

I. There is a high positive correlation between the number of days that have passed since the box of dishwasher powder was opened and the amount of powder left in the box.

II. A scatterplot with days since purchase as the explanatory variable and amount of dishwasher powder used as the response variable would display a strong positive association.

III. The correlation between the amount of powder left in the box and the amount of powder used should be −1.

(a) I only         (d) II and III only

(b) II only         (e) I, II, and III

(c) III only

ANSWER:

Step 1 of 2

Given: A consistent amount of powder is dispensed each night.

Since a consistent amount is dispensed each night, the amount of powder used should increase as the number of days increase and thus there is a positive correlation between the number of days and the amount of powder used.

Since the amount of powder left in the box is the initial amount of powder in the box decreased by the amount of powder used, the amount of powder left will decrease as the amount of powder used increases (note: by the same amounts') and thus there should be a perfect negative correlation between the amount of powder used and the amount of powder left, which has a correlation coefficient of .

Since there is a positive correlation between number of days and the amount of powder used and since there is a negative correlation between amount of powder used and amount of powder left, we expect a negative correlation between number of days and amount of powder left.

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