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The data was collected from approximately 300 students ranging from 8 years old to 12 years old. The pre-test was given during the month of August 1998 and the post-test was given in December of the same year. Scores were collected from all participating students, but only those pieces of the data that had a paired score were included in the analysis. The resulting population consisted of 233 students.
The inferential method used to compare the means of the two populations is often referred to as the paired z-test. This method was chosen because of the large population size, and because the samples were paired. This analysis was also chosen because the distributions of the populations were different.
The assumption was made that data was drawn from a large population size. Below is a frequency distribution of the pre-test and posttest scores, with 0 being the lowest score and 9 being the maximum obtainable score.
Side-by-side histograms of the distributions are given below.
The mean pretest score is 4.320; the mean posttest score is 7.779. The mean of the difference between the pretest and posttest scores is 3.459 and the standard deviation of the differences is 2.058.
A large-sample hypothesis test for the means of two populations using paired data was performed using null hypothesis of H0µJ = 0. In words, there is no significant difference in the means of the pretest and posttest scores. The alternative to the null hypotheses is that there is a significant difference in the means of the pretest and posttest scores. A two-tailed hypothesis was performed at the 5% significance level. The value of the test statistic exceeded the 1.96 critical value. Hence, the test results are statistically significant at the 5% level.
Therefore, at the 5% significance level the data provides sufficient evidence to conclude that there is a difference in the means of the pretest and posttest scores.
- Marty Gorman, M.A., and Stacy West, Texas Women’s University
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