Question

The effectiveness of two speed reading programs is being compared. Ten pairs of people are randomly selected; each pair consists of people whose present reading speeds are essentially identical. From each pair, one person is randomly selected to take Program 1; the other person takes Program 2. After the speed reading programs are completed, the reading speeds, in words per minute, for the 10 pairs of people are found. At the 10% significance level, can we conclude that there is a difference in effectiveness of the two speed reading programs? (Assume that the populations being sampled are approximately normally distributed.) Perform a complete hypothesis test.

Answer 1

To perform a complete hypothesis test for the effectiveness of the two speed reading programs, use a paired t-test and compare the p-value to the significance level.

Step-by-step explanation:

To perform a complete hypothesis test for the effectiveness of the two speed reading programs, we can use a paired t-test. The null hypothesis (H0) would be that there is no difference in effectiveness between the two programs, while the alternative hypothesis (Ha) would be that there is a difference in effectiveness. The significance level is 10%.

To calculate the test statistic, we would need the sample data (reading speeds) for each program. With the sample data, we can then calculate the mean difference, standard deviation, and the t-test statistic.

Next, we determine the degrees of freedom, which is the number of pairs minus 1. Using the degrees of freedom and the t-test statistic, we can find the p-value. If the p-value is less than the significance level (10%), we reject the null hypothesis and conclude that there is a difference in effectiveness between the two programs. Otherwise, we fail to reject the null hypothesis.