• Complete a simulation-based hypothesis test involving a single proportion

Simulation-Based Hypothesis Test

Step 1 of any hypothesis test is to write out the null and alternative hypotheses.

The null hypothesis, [latex]H_{0}[/latex], is what we assume to be true to begin with. It is often a statement of no change from the previous value or from what is expected.

• The null hypothesis, [latex]H_{0}[/latex], is always given in the form: [latex]p = \text{null value}[/latex].

The alternative hypothesis, [latex]H_{A}[/latex], is what we consider to be plausible if the null hypothesis is false. Often, it is a change from the null hypothesis that we would like to test the accuracy of.

• The alternative hypothesis, [latex]H_{A}[/latex], is always given as an inequality: [latex]p > \text{null value}, p < \text{null value}[/latex], or [latex]p \neq \text{null value}[/latex].

In order to conduct a hypothesis test, we have to check the assumptions/conditions for the hypothesis test (Step 2). However, in a simulation-based hypothesis testing, it allows us to conduct the hypothesis test with very few assumptions and have an intuitive result that can be easily interpreted.

Because we are using a simulation, we also no longer need to calculate the test statistics and use our simulated data set to calculate the proportion of the simulated distribution above a certain value as the estimated P-value. We can then use the P-value to determine the strength of evidence the data provide against the null hypothesis.

Let’s use a coin to simulate sampling [latex]16[/latex] questions and counting the number of those questions with “false” as the correct answer in the statistical tool below.
Step 1: Set the Population Proportion to [latex]0.5[/latex]. This represents the probability that a coin lands on “heads.”
Step 2: Set the Sample Size to [latex]16[/latex]. This is the number of times we would like to flip the coin.
Step 3: Under “Select how many samples you want to simulate drawing from the population,” select “[latex]1[/latex]” or “[latex]1000[/latex]” accordingly and click “Draw Sample(s).”
Step 4: Select “Show Distribution of Successes.” The “Sampling Distribution of Number of Successes” shown at the bottom of the page displays how the number of true/false questions with “false” as the correct answer varies across the simulated trials of selecting [latex]16[/latex] questions.
Step 5: Use the “Find Probability for Samp. Dist.” option in the tool to count the proportion of simulated samples to find the P-value.

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