Make a decision to either REJECT or FAIL-TO-REJECT a hypothesis that a population parameter equals a particular value. Do this while setting the proportion of samples in which rejection occurs when the hypothesis is true to a pre-determined value.The proportion of samples in which FALSE rejection occurs is called the level of significance of the test, usually denoted . We also call this the probability of a Type I error. A Type II error is failing to reject the hypothesis when it is actually false.
When constructing a confidence interval, the interval depends on the sample and so it is random. When conducting a hypothesis test, the decision (reject or fail-to-reject) depends on the sample and so the decision made is random before the sample is drawn.
di invnorm(.95)
(yes,
.95 not .90 because this example is a two-sided test).
So part five of the five required elements would be:
Example Crticical Region: Reject H0 if |zcalc| > 1.645.Given your data, you calculate the test statistic and find it equals 0.731. Therefore, you could complete this test in the following way: The value of the test statistic in the sample is .731. Since |.731| is < 1.645, I fail to reject the null hypothesis. . Here is a picture that goes along with this decision.
di 2*normprob(-.731)
.
Either way, you find that the area of the region
equals .465. That is, there is a .465 chance that a
Z random variable will take on a value greater in
absolute value than .731.
This would be the p-value
of the calculated test statistic.Notice that .465 is greater than alpha = .1, which is the area corresponding to P(|Z|>1.645).
Suppose Stata tells you the p-value of a calculate test statistic. Looking at the figure above you should be able to see that you can make the decision about the hypothesis test without checking whether the calculated value lands in the critical region or not. If the p-value is greater than , then we know that we should fail to reject H0. On the other hand, if the p-value is less than then this means the calculated test statistic does lie in the critical region and we should reject H0.