Unformatted text preview: IV. Inference.
A. Confidence Intervals for Population Mean. (Chapter 8) 8) B. Hypothesis Tests of Population Mean (Chapter 9) 1. Basics of Hypothesis Testing 2. Errors, Terms and Conclusions 3. Hypothesis tests: Z-test or t-test (is σX known?) Zt4. Prob Values (P-values) (P5. Type I and Type II Error Probabilities and Power of the Test 6) Write your conclusion - A stand-alone
statement: • Reject H0 : • Fail to Reject H0 : 1 Example: Hypothesis Test Start to Finish.
Cell Cell phone drivers – are they impaired? impaired Compare Compare – cell phone drive to a “baseline driver” and an “intoxicated driver.” Data Data collection: controlled experiment of 40 men and women using driving simulator men and women using a driving simulator. Results: Results: cell phone drivers did worse than the intoxicated drivers on average in breaking reaction time and number of accidents.
Strayer, Drews and Crouch. “A Comparison of the Cell Phone Driver and the Drunk Driver.” Univ. of Utah. Example: Hypothesis Test Start to Finish. Research question: Do cell phone drivers perform worse than intoxicated drivers? The mean breaking response time for intoxicated drivers was 779 ms. 1) Hypothesis – Null and Alternative. Null Hypothesis: Alternative Hypothesis: 2) Choose α: α = 0.05 3) Critical Value(s): Value(s): Hypothesized Hypothesized Sampling Distribution Or:
Standardized Test: 2 4) Estimate: Sample of 40 cell phone drivers had a sample mean of 849 ms and an estimated standard error of 36 ms. tcalc = X − μ0 sX n 5) Compare – complete the Standardized t-test: Standardized t- 6) Conclusion? 4. P-Values: Another way to test hypotheses. 1) State the hypothesis: one or two-tail. 2) Choose α 3) Calculate test statistic from your sample. 4) Determine the P-Value for your test statistic (area in both tails for a 2-tail test). 5) Compare P-Value to α
• • If P-Value < α ; Reject H0 This is no different than finding: One tail-test: | zcalc | is farther into tail than | zα | Two tail-test: | zcalc | is farther into tail than | zα/2 | 6) State your conclusion. 3 4. • • • P-Values: Another way to test hypotheses. Two-Tail Test, α = 0.10. Calculate the test statistic: Eg. zcalc = 1.50. P-Value: 5. Type I Error, Type II Error and Power of the Test Type I Error – P(Type Error) P(Type I Error) = If a Type I Error only concern, then … You never know if the null hypothesis is true – there’s another possible error. Type II Error: P(Type II Error) = II Error) Trade-Off: 4 Example: Manufacture wants to find out if their light bulb lasts longer than 700 hours. 1) Hypothesis:
• Null Hypothesis: • Alternative Hypothesis: 2) Choose level of significance: 3) Critical value(s): • Illustrate – Type I Error • Assume H0 is wrong – Illustrate Type II Error. hours • H0 still wrong. • Now, decrease the level of significance. hours • Illustrate the power of the test: P(Reject False H0 ) 5 ...
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- Spring '11
- Null hypothesis, Statistical hypothesis testing, type ii error, cell phone driver, cell phone drivers