# A sample of freshmen takes a reading comprehension test and their scores are summarized below

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 deviation_{}is 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.

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