# What’s a P-Value Anyway?

You are a recent graduate and have been hired by John Jolly to run and interpret a t-test. John is the owner of John’s Jolly Small Aircraft Quick Oil Change. John is experimenting with a new oil change process and is trying to determine if the current process takes more time than the new process he is experimenting with. 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 (α = .05).
t-Test: Two-Sample Assuming Unequal Variance
Current Process New Process
Mean 30.15 14.20
Variance 234.8710526 14.16842105
Observations 20 20
Hypothesized Mean Difference 0
df 21
t Stat 4.520032841
P(T<=t) one-tail 9.37197E-05 t Critical one-tail 1.720742903 P(T<=t) two-tail 0.000187439 t Critical two-tail 2.079613845 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?" You know John is not reading the p-value correctly (due to his misinterpretation of the E-05 at the end of the p-value number). How will you explain the results to John? Watch & Answer First, watch this video to become familiar with running and interpreting a t-test in Excel. Hypothesis Test for 2 Population Means using Excel's Data Analysis (YouTube 5:39) (https://youtu.be/_WNUfgZipww) 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? (Remember to interpret what the E-05 means and round to 3 decimal places) Do you think (as John does) that the result is not statistically significant? Do the results “prove” anything?