A national reading achievement test is standardized such that the mean score for the population of seventh-grade students is equal to 100. A researcher selects a sample of 25 seventh-grade students and enrolls them in a special reading course.
After 6 weeks, the students in the sample take the standardized test. The mean for the sample is 112.
Based solely on the sample mean, can the researcher conclude that the special training has an effect on reading achievement? Explain your answer.
(Hint: If the course has no effect, how can you explain the 12-point difference between the sample mean and the population mean?)