Testing the Difference Between Two Fire Stations' Response Times

How can you test the difference between the means of the two fire stations' response times? A two-sample t-test can be used to test the difference between the means of the two fire stations' response times. The t-test will compare the difference between the sample means of the response times to the standard error of the difference. If the t-statistic calculated from the test is greater than the critical value from a t-distribution table with degrees of freedom equal to the sum of the degrees of freedom of the two samples minus two, then the null hypothesis can be rejected, and it can be concluded that there is a significant difference in the mean response times between the two fire stations.

What is a Two-Sample T-Test?

A two-sample t-test is a statistical test to determine if the means of two independent groups are significantly different from each other. In this case, the two independent groups are the response times of the two fire stations. The t-test calculates the difference between the means of the two samples relative to the variability within the samples.

Null Hypothesis and Alternative Hypothesis

Null hypothesis: There is no difference in the mean response times between the two fire stations.

Alternative hypothesis: There is a difference in the mean response times between the two fire stations.

Interpreting the Results

After conducting the two-sample t-test, the results will provide a t-statistic value. By comparing this value to the critical value from a t-distribution table, you can determine whether to reject the null hypothesis. If the calculated t-statistic is greater than the critical value, it indicates that there is a significant difference in the mean response times between the two fire stations.

Conclusion

The two-sample t-test is a powerful statistical tool to compare the means of two groups and determine if there is a significant difference between them. In the case of the fire stations' response times, this test can provide valuable insights into whether there are variations in their performance levels.

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