Question

Which of the following conclusions seems most justified?

(a) The mean fear ratings increased from $1989to1991$, because the slope of the least-squares line is positive.

(b) It appears that children with high fear ratings in $1989$ had lower ratings in $1991$.

(c) It appears that children with high fear ratings in$1989$had higher ratings in $1991$.

(d) There is no evidence of a significant relationship between the mean fear ratings in $1989$ and in $1991$.

(e) There are sufficient inconsistencies in the data to make it impossible to draw any conclusions.

Short answer

The correct answer is option (b) is it appears that children with high fear ratings in $1989$had lower ratings in$1991$.

Step-by-step solution

Part (a) step 1: Given Information

We need to find the mean fear ratings increased from $1989to1991$, because the slope of the least-squares line is positive.

Part (a) step 2: Explanation

By observing the given conclusion the mean fear ratings increased from 1989 to 1991, because the slope of the least-squares line is positive, not justified.

Part (b) step 1: Given Information 

We need to find It appears that children with high fear ratings in $1989$ had lower ratings in $1991$.

Part (b) step 2: Simplify

It appears the children with high fear ratings in $1989$has lower ratings in $1991$, because most children with a$1989$mean rating over$2.0$, so a$1991$mean rating below$2.0$.

Part (c) step 1: Given Information 

We need to find it appears that children with high fear ratings in$1989$had higher ratings in $1991$.

Part (c) step 2: Explanation

By observing the given conclusion it appears that children with high fear ratings in$1989$had higher ratings in $1991$ are not correct.

Part (d) step 1: Given Information 

We need to find there is no evidence of a significant relationship between the mean fear ratings in $1989$and in $1991$.

Part (d) step 2: Explanation

By observing the given conclusion there is no evidence of a significant relationship between the mean fear ratings in $1989$and in $1991$is not correct.

Part (e) step 1: Given Information

We need to find there are sufficient inconsistencies in the data to make it impossible to draw any conclusions.

Part (e) step 2: Explanation

By observing the given conclusion there are sufficient inconsistencies in the data to make it impossible to draw any conclusions not correct.