A sample of freshmen takes a reading comprehension test and their scores are summarized below. If the mean for the general population on this test is m = 12, can you conclude that this sample is significantly different from the population. Test with a = .05.
Sample Scores: 16, 8, 8, 6, 9, 11, 13, 9, 10
Solution: From the data we have that
We want to test following null and alternative hypotheses
Since the population standard deviationis unknown, we are can use a t-test. In fact, we’ll use a two-tailed t-test. The t-statistics is given by the following formula:
The two-tailed critical t-value for and degrees of freedom is equal to
Since, we fail to reject the null hypothesis. This means that we don’t have enough evidence to support the claim that this sample is significantly different from the population, at the significance level.