Q. 47 - The Practice of Statistics for AP

Question

North Carolina State University studied student performance in a course required by its chemical engineering major. One question of interest was the relationship between time spent in extracurricular activities and whether a student earned a C or better in the course. Here are the data for the 119 students who answered a question about extracurricular activities:

(a) Calculate percentages and draw a bar graph that describes the nature of the relationship between time spent on extracurricular activities and performance in the course. Give a brief summary in words. 

b) Explain why you should not perform a chi-square test in this setting. 

Step-by-Step Solution

Answer

(a) The most proportion of passing grades is obtained if the activities are between $2$and $12$ hours per week. The least proportion of passing grades is obtained if the activities are more than $12$ hours per week.

The bar graph is 

(b) Expected values not all at least $5.$

Part (a) Step 1: Given information

The given data is

Part (a) Step 2: Explanation

The proportions in each group are the number of subjects divided by the column total

Create a histogram

The width of each bar is equal and the height is equal to the proportion.

The most proportion of passing grades are obtained if the activities are between $2$ and $12$ hours per week. The least proportion of passing grades are obtained if the activities are more than $12$ hours per week.

Part (b) Step 1: Given information

The given data is

Part (b) Step 2: Explanation

The chi-square test requires that the expected values are at least 5 .

We note that the column total for $>12$ is $8$ and thus at least one of the expected counts for $>12$ is less than $5$ .

Thus the chi-square test cannot be applied.

Expected values not all at least 5 .