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 the 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.

$$\begin{gathered} \left(a\right)Ionly\left(c\right)IIIonly\left(e\right)I,II,andIII \\ \left(b\right)IIonly\left(d\right)IIandIIIonly \end{gathered}$$

Step by step solution

01

Given information

Mr. Kleen puts dishwasher powder in his dishwasher every night before going to bed.

02

Concept

The correlation coefficient reflects how closely the two variables are related linearly.

03

Explanation

It's difficult to have a positive association. As a result, my statement I is false. The amount of dishwasher powder used increases as the days following purchase increase, indicating a significant positive relationship. As a result, assertion II is correct. Because as the amount of powder used grows, the amount of powder left in the box decreases, and the amount of powder left in the box should be perfectly negatively linked. As a result, assertion$III$is likewise correct. As a result, option (d) is right. $OnlyIIandIIIarecovered$

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