A study in Orlando, Florida claimed that the mean commute time for all employees working at Disney exceeds 40 minutes. This figure is higher than what was assumed in the past. The plan is to test this claim at a level of significance = 0.05 and a sample size = 100 commuters. For this sample size, it was found the sample mean is 43.5 minutes. Based on previous studies, assume the standard deviation is known to be o = 8 minutes. Conduct a hypothesis test using a rejection region and draw a conclusion.

(please provide complete detailed answer)

Use a one-sample z-test.

z = (sample mean - population mean)/(standard deviation divided by the square root of the sample size)

With your data:
z = (43.5 - 40)/(8/√100) = ?

Finish the calculation.

Check a z-table at .05 level of significance for a one-tailed test.
If the z-test statistic exceeds the critical value from the z-table, reject the null. If the z-test statistic does not exceed the critical value from the z-table, do not reject the null.

I hope this will help get you started.

To conduct a hypothesis test in this scenario, we need to set up the null (H0) and alternative (Ha) hypotheses, determine the level of significance, calculate the test statistic, find the critical value(s), and make a decision based on the results.

Here are the steps to follow:

Step 1: Formulate the hypotheses:
Null hypothesis (H0): The mean commute time for all employees working at Disney is not greater than 40 minutes. (μ <= 40)
Alternative hypothesis (Ha): The mean commute time for all employees working at Disney exceeds 40 minutes. (μ > 40)

Step 2: Determine the level of significance:
The level of significance, denoted as α (alpha), is given as 0.05, which means we want to conduct the test at a 95% confidence level. This implies that if the p-value is less than 0.05, we will reject the null hypothesis.

Step 3: Calculate the test statistic:
In this case, since the population standard deviation is known (σ = 8 minutes), we can use a z-test. The test statistic formula is:
z = (sample mean - population mean) / (population standard deviation / √sample size)
z = (43.5 - 40) / (8 / √100)
z = 3.5 / 0.8
z = 4.375

Step 4: Find the critical value(s):
Since our alternative hypothesis is one-tailed (Ha: μ > 40), we need to find the critical value for a right-tailed test at a significance level of 0.05. The critical value zα is the value that separates the rejection region from the acceptance region.

Using a standard normal distribution table or calculator, we find the critical value for α = 0.05 to be approximately 1.645 (rounded to three decimal places).

Step 5: Make a decision:
If the test statistic (z = 4.375) is greater than the critical value (1.645), we will reject the null hypothesis (H0). Otherwise, if the test statistic is less than or equal to the critical value, we will fail to reject the null hypothesis.

In this case, 4.375 > 1.645, which means the test statistic falls in the rejection region. Therefore, we reject the null hypothesis.

Step 6: Conclusion:
Based on the sample data and hypothesis test, there is enough evidence to support the claim that the mean commute time for all employees working at Disney exceeds 40 minutes.