ABSTRACT
Suppose a researcher selected a random sample of first-grade girls and a random sample of first-grade boys from a large school district in order to estimate the average reading achievement of each sample on a standardized test. Further, suppose the researcher obtained these means:
Girls Boys m = 50.00 m = 46.00
This result suggests that girls, on the average, have higher achievement in reading than boys. But do they really? Remember that the researcher tested only random samples of the boys and the girls. Thus, it is possible that the difference the researcher obtained is due only to the errors created by random sampling, which are known as sampling errors. In other words, it is possible that the population mean for boys and the population mean for girls are identical and that the researcher found a difference between the means of the two randomly selected samples only because of the chance errors associated with random sampling. This possibility is known as the null hypothesis. For the difference between two sample means, it says that:
The true difference between the means (in the population) is zero.
