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Chapter 11: Q. 47 (page 728)

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.

Short Answer

Expert verified

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

The bar graph is

(b) Expected values not all at least5.

Step by step solution

01

Part (a) Step 1: Given information

The given data is

02

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

03

Part (b) Step 1: Given information

The given data is

04

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 >12is 8and thus at least one of the expected counts for >12is less than 5.

Thus the chi-square test cannot be applied.

Expected values not all at least 5 .

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