Stats 1
Stats 2
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AS/A2 Stats 1 Stats 2 |
| S3 Topic 3: Estimation, confidence intervals and tests | |
| Hypothesis tests for the mean of a Normal distribution with variance known |   |
| The experiment is to
select a random sample of size n from a selected distribution and then test a
hypothesis about the mean µ at a specified significance level.
Either the normal, gamma, and uniform distributions can be selected from a list box. The appropriate parameters (m and s for the normal distribution) and the sample size n can be varied with scroll bars. The significance level can be selected with a list box, as can the type of test: two-sided, left-sided, or right-sided. The boundary point µ0 between the null and alternative hypotheses can be varied with a scroll bar. The density of the distribution and µ are shown in blue in the first graph; µ0 is shown in green. The test can be constructed under the assumption that the distribution standard deviation is known or unknown. In the first case, the test statistic has the standard normal distribution; in the second case the test statistics has the student t distribution with n - 1 degrees of freedom. The density and the critical values of the test statistic are shown in the second graph in blue. On each update, the sample density is shown in red in the first graph and the sample values are recorded in the first table. The sample mean M is shown in red in the first graph and the value of the test statistics (Z or T) is shown in red in the second graph. The variable I indicates the event that the null hypothesis is rejected. On each update, M, Z or T, and I are recorded in the second table. Note that the null hypothesis is reject (I = 1) if and only if the test statistic (Z or T) falls outside of the critical values. Finally, the empirical density of I is shown in red in the last graph and recorded in the last table. |
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An applet freely
available from