# One-tailed and Two-tailed

What is the difference between the null and alternative hypothesis statements in one tailed and two tailed tests? How can manufacturing companies use the standard normal distribution to determine quality control of their products?

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(1) If the question asks us to determine if there is a difference between the statistic and a value, then we have a two-tail test. In this case, the null hypothesis will be, for example, Mean = some value v, whereas the alternate hypothesis will be Mean ≠ v. A simple example will be to test if the mean marks of a class in a Math quiz is 8 or not. ***

If the question asks us to determine if the difference between the statistic and a value is > 0 or < 0, that is positive or negative, then we have a one-tail test. Consider a situation where we are testing to see if a steel bolt can withstand a stress of 1000 N/mm^2. If it does, then it will be used. Otherwise not. Here, a two-tailed test (H0: stress withstood ≠ 1000 vs Ha: stress withstood = 1000) ...

#### Solution Summary

Neat and elaborate discussion of both the questions with examples.