Application
(a) Open the FakeSleepDeprivation.xls. Load these data into the Multiple Means applet below and produce graphical and numerical summaries as before.
Include a screen capture of your output in your report.
(b) How do these data compare to the actual study data (e.g., shape, center, spread)?
(c) Using the same null and alternative hypotheses, conjecture how the statistical significance of these hypothetical data will compare to that of the actual study data (e.g., larger p-value, smaller p-value, same p-value). Briefly explain your reasoning. (Hint: Will there be more, less, or the same strength of evidence against the null hypothesis?)
(d) Use this applet to carry out the randomization test:
- Check the Show Shuffle Options box.
- Scroll to the right.
- Select the Plot radio button and press Randomize a few times. Notice how the red and black dots switch group labels at random.
- Now generate at least 1000 random shuffles.
- Use the Count Samples box testimate the p-value.
Include a screen capture of your output in your report.
(e) How does the p-value compare to that of the actual study data (larger, smaller, the same)? Is this what you conjectured?
(f) Create an informal confidence interval using the 2SD short-cut. Show your work. Does the confidence interval change? If so how (midpoint? width?)?
(g) Explain why these changes (or lack of changes) to the test statistic, p-value, and confidence interval make intuitive sense (based on your observations in part (a) of the Application).
