# I am not quite sure what the difference is between the null and alternative hypotheses statements in one-tailed and two-tailed tests? Can you help?

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### 2 Answers

The null hypothesis is generally that the variable being studied is unchanged. (For example, we are told that the population mean is `mu=10` Then the null hypothesis is `H_0: mu=10` )

In a one-tailed test, we are seeking to find if the variable is greater than or less than the given value. (For the example above, we assert that `H_1:mu<10` or `H_1: mu>10` as our alternative hypothesis.)

In a two-tailed test we assert that the variable is either greater than or less than the given value. (For the example above `H_1: mu != 10` is the alternative hypothesis.)

The effect is on the critical value. For a one-tailed test, if we are at the 90% significance level we have a critical value where 90% of z scores are beneath (or 10% if less than). For a two-tailed test we have a critical value where 95% is below and 5% below. (This is because the critical region is to be 10% of the area under the curve -- 5% is to the left and 5% to the right.)

Thank you so much for your help. I can understand it a little more each time my question is answered. Thanks again!