Complete the following steps to interpret a randomization test for 2-sample means. 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 the chosen statistic from each resample. The bootstrap distribution should appear to be normal. If the bootstrap distribution is non-normal, you cannot trust the bootstrap results.

To determine whether the difference between population means 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 means is statistically significant. To calculate a confidence interval and determine whether the difference is practically significant, use Bootstrapping for 2-sample means. 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 means is statistically significant.

μ₁: population mean of Rating when Hospital = A |
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µ₂: population mean of Rating when Hospital = B |

Difference: μ₁ - µ₂ |

Hospital | N | Mean | StDev | Variance | Minimum | Median | Maximum |
---|---|---|---|---|---|---|---|

A | 20 | 80.30 | 8.18 | 66.96 | 62.00 | 79.00 | 98.00 |

B | 20 | 59.30 | 12.43 | 154.54 | 35.00 | 58.50 | 89.00 |

Mean of A - Mean of B = 21.000 |
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Null hypothesis | H₀: μ₁ - µ₂ = 0 |
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Alternative hypothesis | H₁: μ₁ - µ₂ ≠ 0 |

Number of Resamples | Average | StDev | P-Value |
---|---|---|---|

1000 | -0.185 | 4.728 | < 0.002 |

In these results, the null hypothesis states that the difference in the mean rating between two hospitals is 0. Because the p-value is less than 0.002, which is less than the significance level of 0.05, the decision is to reject the null hypothesis and conclude that the ratings of the hospitals are different.