The Sign Test Experiment

]> The Sign Test Experiment

Description

The experiment is to select a random sample of size $n$ from a distribution, and then to perform a hypothesis test about the median $m$ of the distribution at a specified significance level. The distribution can be selected from a list box; the options are the normal, gamma, and uniform distributions. In each case, the appropriate parameters and the sample size $n$ can be varied with scroll bars.

The significance level can be selected with a scroll bar. The null hypothesized value $m 0$ of the median can be selected with a scroll bar; the true quantile level $p$ of $m 0$ is also given. The probability density function of the distribution and the median $m$ are shown in blue in the first graph; $m 0$ is shown in green.

The test statistic $N$ is the number of sample values greater than $m 0$ . Under the null hypothesis, $N$ has the binomial distribution with parameters $n$ and $1 2$ . The probability density function of this distribution and the critical values are shown in the second graph in blue.

On each update, the sample density function is shown in red in the first graph and the sample values are recorded in the sample table. The value of the test statistics $N$ is shown in red in the second graph.Random variable $J$ indicates the event that the null hypothesis is rejected. On each update, $N$ and $J$ are recorded in the data table. Note that the null hypothesis is rejected ( $J 1$ ) if and only if the test statistic $N$ falls outside of the critical values. Finally, the empirical probability density of $I$ is shown in red in the distribution graph and recorded in the distribution table.