Chapter 6.1, Problem 35E

(a)

To determine

Whether students tend to have higher reading scores after participating in the chess program.

Answer to Problem 35E

Yes, the students tend to have higher reading scores after participating in the chess program.

Explanation of Solution

Given information:

From the figure,

We can see that

The boxplot of Posttest lies slightly higher than the boxplot of Pretest.

Also,

The most of the boxplot of “Post − Pre” lies above 0.

Thus,

The students tend to have higher reading scores after participating in the chess program.

Moreover,

In the descriptive statistics,

We came to know that

All descriptive statistics of Posttest are greater than the corresponding descriptive statistics of Pretest (except for the maximum).

Also,

All descriptive statistics of Post − Pre are positive (except for the minimum and first quartile).

Thus,

This confirms our conclusion.

(b)

To determine

Whether it can be concluded that playing chess causes an increase in reading skills.

Answer to Problem 35E

No, we cannot conclude that playing chess causes an increase in reading skills.

Explanation of Solution

Given information:

In Part (a),

We concluded that

Students tend to have higher reading scores after participating in the chess program.

However,

Since the study did not include a control gap,

The association does not necessarily mean causation.

This implies

The statistically significant improvement could be due to some other lurking variable (like experience or age) instead of the treatment.