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.