Chapter 11: Q 25. (page 718)

Do students who read more books for pleasure tend to earn higher grades in English? The boxplots show data from a simple random sample of $79$ students at a large high school. Students were classified as light readers if they read fewer than $3$ books for pleasure per year. Otherwise, they were classified as heavy readers. Each student’s average English grade for the previous two
marking periods was converted to a GPA scale, where $A = 4.0, A - = 3.7, B + = 3.3$
Reading and grades (10.2) Summary statistics for the two groups from Minitab are provided.
a. Explain why it is acceptable to use two-sample $t$ procedures in this setting.
b. Construct and interpret a $95 %$ confidence interval for the difference in the mean English grade for light and heavy readers.
c. Does the interval in part (b) provide convincing evidence that reading more causes a difference in students’ English grades? Justify your answer.

Short Answer

Expert verified

Part (a) All conditions satisfied so it is acceptable to use two-sample t test.

Part (b) The $95 %$ confidence interval for the difference in the mean English grade for light and heavy readers is $(0.1254, 0.4426)$

Part (c) There is enough evidence that reading more causes a difference in student’s English grades.

Step by step solution

Part (a) Step 1: Given information

The box plot:

Summary statistic:

Part (a) Step 2: Explanation

If and only if these requirements are met, a two-sample t-test will be appropriate. Because the sample is a random sample, the random criterion is met. The box plot outliers are minor, and the sample size is more than $30$ therefore the normal criterion is also met. Because the sample sizes of $47$ and $32$ are both less than $10 %$ of the population, the independent condition is likewise met. Therefore, it is acceptable to use two sample t-test.