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Answer :
To assess if the average escape time exceeds 6 minutes, a hypothesis test with a. H0: μ = 360; Ha: μ > 360 should be conducted using a one-sample Z-test.
To determine if the data contradicts the investigators' prior belief that the true average escape time would be at most 6 minutes (360 seconds), we need to conduct a hypothesis test. Given the sample mean of escape time is 371.84 seconds and the sample standard deviation is 24.89 seconds. The significance level (alpha) is set at 0.05.
The null hypothesis (H0) represents the status quo or the claim to be tested, while the alternative hypothesis (Ha) represents what we aim to support with evidence. Based on the simulated exercise:
Step 1: State the Null and Alternative Hypothesis
- H0: μ = 360
- Ha: μ > 360
In this case, the null hypothesis claims that the mean is equal to 360 seconds, and the alternative hypothesis claims that the mean is greater than 360 seconds.
Step 2: Select the Appropriate Test
Assuming normality, we should apply a one-sample Z-test because the sample size is greater than 30 and the population standard deviation is unknown, but we approximate it with the sample standard deviation.
Step 3: Conduct the Test and Make a Decision
After calculating the test statistic and comparing it to the critical value associated with a significance level of 0.05, we will be able to make a decision whether to reject or not reject H0.
If the test statistic is greater than the critical value, we reject H0 and support Ha, suggesting that the data does contradict the prior belief that the true average escape time is at most 6 minutes. If not, we fail to reject H0.
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