One would expect a student to be able to guess the answers to 10 items on a 20-item true-false test. The scores for 14 students on a 20-tiem true-false test follow. Please test the null hypothesis that the population mean of guess answers equals 10, against the non-directional alternative hypothesis. Use p < .05.
Solution: We have to test the hypotheses
In order to test the null hypothesis we use a two-tailed t-test, for the significance level. The data and the basic statistics are summarized in the following table
The t-statistics is computed as
The critical level forand 13 degrees of freedom are. Since, we reject the null hypothesis, which means that we have enough evidence to claim that the population mean of guess answers is not equal to 10, at the 0.05 significance level.