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

Use the histogram to examine the shape of your bootstrap distribution. The bootstrap distribution is the distribution of means 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.

To determine whether the difference between the population mean and the hypothesized mean 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 means is statistically significant (Reject H
_{0}) - 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 mean and the hypothesized mean is statistically significant. To calculate a confidence interval and determine whether the difference is practically significant, use Bootstrapping for 1-sample function. For more information, go to Statistical and practical significance.
- P-value > α: The difference between the means is not statistically significant (Fail to reject H
_{0}) - 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 mean and the hypothesized mean is statistically significant.

Observed Sample
Variable N Mean StDev Variance Sum Minimum Median Maximum
Time 16 11.331 3.115 9.702 181.300 7.700 10.050 16.000

Randomization Test
Null hypothesis H₀: μ = 12
Alternative hypothesis H₁: μ < 12

Number of
Resamples Mean StDev P-Value
1000 11.9783 0.7625 0.199

In these results, the alternative hypothesis states that the mean reaction time is less than 12 minutes. Because the p-value is 0.203, which is greater than the significance level of 0.05, the decision is to fail to reject the null hypothesis. You cannot conclude that the mean reaction time is less than 12 minutes.