Interpret the key results for Randomization Test for 1-Sample Proportion

Complete the following steps to interpret a randomization test for 1-sample proportion. Key output includes the histogram and the p-value.

Step 1: Examine the shape of your bootstrap distribution

Use the histogram to examine the shape of your bootstrap distribution. The bootstrap distribution is the distribution of proportions from each resample. The bootstrap distribution should appear to be normal. If the bootstrap distribution is non-normal, you cannot trust the results.
50 resamples
1000 resamples

The distribution is usually easier to determine with more resamples. For example, in these data, the distribution is ambiguous for 50 resamples. With 1000 resamples, the shape looks approximately normal.

In this histogram, the bootstrap distribution appears to be normal.

Step 2: Determine whether the test results are statistically significant

To determine whether the difference between the population proportion and the hypothesized proportion is statistically significant, compare the p-value to the significance level. Usually, a significance level (denoted as α or alpha) of 0.05 works well. A significance level of 0.05 indicates a 5% risk of concluding that a difference exists when there is no actual difference.
P-value ≤ α: The difference between the proportions is statistically significant (Reject H0)
If the p-value is less than or equal to the significance level, the decision is to reject the null hypothesis. You can conclude that the difference between the population proportion and the hypothesized proportion is statistically significant. To calculate a confidence interval and determine whether the difference is practically significant, use Bootstrapping for 1-Sample Proportion. For more information, go to Statistical and practical significance.
P-value > α: The difference between the proportions is not statistically significant (Fail to reject H0)
If the p-value is greater than the significance level, the decision is to fail to reject the null hypothesis. You do not have enough evidence to conclude that the difference between the population proportion and the hypothesized proportion is statistically significant.
Randomization Test
Number of Resamples
Average
P-Value
Key Results: P-Value

In these results, the alternative hypothesis states that the proportion of readers that own a PlayStation console is greater than 0.5. Because the p-value is 0.002, which is less than the significance level of 0.05, the decision is to reject the null hypothesis and conclude that the proportion of readers that own a PlayStation console is greater than 0.5.

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