Reading Rates (See Problem 22 in Section 10.3.) Michael Sullivan, son of the author, decided to enroll in a reading course that allegedly increases reading speed and comprehension. Prior to enrolling in the course, Michael read 198 words per minute (wpm). The following data represent the words per minute read for 10 different passages after the course.
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a. The goal of the research is to determine if the words read per minute has increased as a result of the reading course. Based on this research objective, state the null and alternative hypotheses.

Verified step by step guidance

1. Identify the parameter of interest: the mean words per minute (wpm) read after the course.
2. Define the null hypothesis (\(H_0\)) as the statement that the reading course has no effect or has not increased the reading speed. Mathematically, this means the mean wpm after the course is less than or equal to the mean wpm before the course: \(H_0: \mu \leq 198\).
3. Define the alternative hypothesis (\(H_a\)) as the statement that the reading course has increased the reading speed. This means the mean wpm after the course is greater than the mean wpm before the course: \(H_a: \mu > 198\).
4. Note that this is a one-tailed test because the research objective is specifically to determine if the reading speed has increased, not just changed.
5. These hypotheses set the framework for conducting a statistical test (such as a one-sample t-test) to evaluate whether the observed data provide sufficient evidence to conclude an increase in reading speed.

Key Concepts

Hypothesis Testing

Hypothesis testing is a statistical method used to decide whether there is enough evidence to reject a null hypothesis in favor of an alternative hypothesis. It involves formulating two competing statements about a population parameter and using sample data to assess their validity.

Null and Alternative Hypotheses

The null hypothesis (H0) represents the status quo or no effect, while the alternative hypothesis (Ha) reflects the research claim or effect. In this context, H0 states that the reading speed has not increased, and Ha states that the reading speed has increased after the course.

One-Sample t-Test for Means

A one-sample t-test compares the sample mean to a known value (here, 198 wpm) to determine if there is a statistically significant difference. It is appropriate when the population standard deviation is unknown and the sample size is small, as with the 10 passages read after the course.