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 for_{}and 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.

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