### Question Description

I’m working on a mathematics question and need an explanation to help me study.

John is the owner of John’s Jolly Oil Change. John is experimenting with a new oil change process and is trying to determine if the new process takes less time than the old process. John is comparing sample mean times to evaluate his hypothesis about the population (total number of oil changes). Over the period of a week, he took a random sample of oil changes using both the old and new processes. Using the information John provided, you ran a t-test for independent samples. These are the results (? = .05).

t-Test: Two-Sample Assuming Unequal VarianceNew ProcessOld ProcessMean14.230.15Variance14.16842105234.8710526Observations2020Hypothesized Mean Difference0df21t Stat-4.520032841P(T<=t) one-tail9.37197E-05t Critical one-tail1.720742903P(T<=t) two-tail0.000187439t Critical two-tail2.079613845

When you begin to share the information with John, he immediately says, “Oh my gosh, look at that P value, it is 9! That is bad, right? What does that E-05 mean at the end of the number?”

How will you explain the results to John?

First, watch this video to become familiar with running and interpreting a t-test in Excel.

Now, think about how you will respond to John. Answer the following questions.

- What is the hypothesis in this scenario?
- Did the new oil change process take less or more time? How do you know?
- In the scenario, did you conduct a one or two-tailed test?
- What is the P value? (Round to 3 decimal places)
- Do you think (as John does) that the result is not statistically significant?
- Do the results “prove” anything?