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# Z-Statistic, T-Statistic and P-value

1. We have now studied two statistics Z and t. Compare and contrast the use of these two statistical tests, with particular attention to the quantity and quality of the data we use in each test. Is one test better than the other?

2. In research the concept of p value is useful to interpret the results of a hypothesis test. Define p value and discuss its relationship to the calculated value of a test statistic such as Z.

If you were reading a professional journal article and saw a p value of0.001 would this support or be inconsistent with the research hypothesis Ha?

#### Solution Preview

1. Both z and t test statistics are based on Normal distribution - however, the z statistic should be used when the population variance (or the standard deviation) is known, whereas a t-statistic is used when the population variance is unknown. Because of this, the t-statistic always has a degree of freedom attached to it, which is equal to one less than the sample size. It is noted, however, that as the sample size ...

#### Solution Summary

This solution of 284 words explains the appropriate usage for the z and t test statistics, the meaning of the p-value and what to expect when seeing a p-value of 0.001.

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