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.

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.

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 |

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.