Based on your results, which of the following is TRUE? Use the significance level of 0.05 for your analysis.a.There is enough evidence to suggest that the average delivery time is longer than 20 minutes.b.There is enough evidence to suggest that the average delivery time is less than 20 minutes.c.There is not enough evidence to suggest that the average delivery time is longer than 20 minutes.d.There is not enough evidence to suggest that the average delivery time is less than 20 minutes.
Question
Based on your results, which of the following is TRUE? Use the significance level of 0.05 for your analysis.a.There is enough evidence to suggest that the average delivery time is longer than 20 minutes.b.There is enough evidence to suggest that the average delivery time is less than 20 minutes.c.There is not enough evidence to suggest that the average delivery time is longer than 20 minutes.d.There is not enough evidence to suggest that the average delivery time is less than 20 minutes.
Solution
To determine which statement is true, we need to conduct a hypothesis test. We are testing the null hypothesis that the average delivery time is 20 minutes against the alternative hypothesis that the average delivery time is more than 20 minutes.
We can use a one-sample t-test for this purpose. The test statistic is calculated as follows:
t = (x̄ - μ) / (s/√n)
where:
- x̄ is the sample mean (20.56 minutes),
- μ is the population mean under the null hypothesis (20 minutes),
- s is the sample standard deviation (2.65 minutes), and
- n is the sample size (168 orders).
First, calculate the test statistic:
t = (20.56 - 20) / (2.65/√168) ≈ 2.76
Next, compare the test statistic to the critical value for a one-tailed t-test with a significance level of 0.05 and degrees of freedom n - 1 = 167. The critical value can be found using a t-table or Excel's T.INV function. For this case, the critical value is approximately 1.65.
Since the test statistic (2.76) is greater than the critical value (1.65), we reject the null hypothesis. This means there is enough evidence to suggest that the average delivery time is longer than 20 minutes.
Therefore, the answer is a. There is enough evidence to suggest that the average delivery time is longer than 20 minutes.
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