Freddy is the owner of Freddy’s fast fuel for Small Aircraft specializing in “Providing flight fit fantastic fuel” for small general aviation aircraft such as a Cessna 172. Freddy is experimenting with a fueling process involving new equipment and is trying to determine if the current process takes more time than the new process with the new equipment he is experimenting with. If the current process takes more time than the new process, Freddy will purchase some new, rather expensive fueling equipment to use across several small general aviation airports his company services. Freddy is comparing sample mean times to evaluate his hypothesis about the population (total number of aircraft fuel fill-ups). Over the period of a week, he took a random sample of fuel fill-up times using both the old and new processes. Using the information Freddy provided, you ran a t-test for independent samples. These are the results (α = .05).
Freddy is the owner of Freddy’s fast fuel for Small Aircraft specializing in “Providing flight fit fantastic fuel” for small general aviation aircraft such as a Cessna 172.
Freddy is experimenting with a fueling process involving new equipment and is trying to determine if the current process takes more time than the new process with the new equipment he is experimenting with. If the current process takes more time than the new process, Freddy will purchase some new, rather expensive fueling equipment to use across several small general aviation airports his company services. Freddy is comparing sample mean times to evaluate his hypothesis about the population (total number of aircraft fuel fill-ups). Over the period of a week, he took a random sample of fuel fill-up times using both the old and new processes. Using the information Freddy 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 | 63.15 | 48.15 |
| Variance | 104.2394737 | 60.87105263 |
| Observations | 20 | 20 |
| Hypothesized Mean Difference | 0 | |
| df | 36 | |
| t Stat | 5.220581451 | |
| P(T<=t) one-tail | 3.82255E-06 | |
| t Critical one-tail | 1.688297714 | |
| P(T<=t) two-tail | 7.64509E-06 | |
| t Critical two-tail | 2.028094001 |
When you begin to share the information with Freddy, he immediately says, "Oh my gosh, look at that p-value, it is 3.8! That is bad, right? What does that E-06 mean at the end of the number?"
You know Freddy is not reading the p-value correctly (due to his misinterpretation of the E-06 at the end of the p-value number). How will you explain the results to Freddy?
Now, think about how you will respond to Freddy. Answer the following questions.
- What is the hypothesis in this scenario?
- Did the new fuel 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-06 means and round to 3 decimal places)
- Do you think (as Freddy does) that the result is not statistically significant?
- Do the results “prove” anything?
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I forgot to ask based on this information do you think another sample should be taken to see if the intial findings can be replicated?
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