Hypothesis Testing: A Concise Statistical Method Reference
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Hypothesis Testing
Statistical Test Selection
1. If the population standard deviation is unknown and the sample size is less than 30: t-test
2. If the population standard deviation is known and the sample size is less than 30: t-test
7. Hypothesis test on population mean; n = 25; σ = 2.5: z-test
8. Hypothesis test on population mean; n = 50; s = 7.2: z-test
18. Test statistic for sample size above 30: z-test
19. Test statistic when population standard deviation is known: z-test
20. Test statistic when population standard deviation is unknown: t-test
21. When to use the t-test: I and II
24. Optimal sample size for z-test: Equal to or larger than 30
Hypotheses and Significance
3. H0: μ = 30
4. H1: μ > 30
5. No
9. False: The alternative hypothesis typically corresponds to the assumption that a change does occur.
12. Level of Significance: The degree of uncertainty about the statistical statement under the same conditions used to determine the confidence level.
26. Correct Decision: Failure to reject a true null hypothesis
27. Significance at 5% Level: There is a 5% probability that a true null hypothesis is rejected.
30. H0: μ < 64", H1: μ > 64"
32. H0: μ = 81.6, H1: μ ≠ 81.6
33. Conclusion: There is not enough evidence to reject the claim.
35. When the null hypothesis is rejected: There is enough evidence against the null hypothesis.
36. Failing to reject the null hypothesis: There is insufficient evidence to disagree with the null hypothesis.
Test Statistics and Critical Values
6. t-test
14. > 1.645
15. z < -2.575 or z > 2.575
16. z > 1.645
17. Test Statistic: A value calculated from sample data, used to decide whether to reject the null hypothesis.
22. t-test
23. 1.190
28. Critical Value: Separates the critical region from the non-critical region in a normal curve during hypothesis testing.
29. Decision when computed z-value lies in the critical region: Reject the null hypothesis
34. Right-tailed test, critical value > computed value: Do not reject the null hypothesis
37. t-computed = 1.093, critical value = 1.699: Do not reject the null hypothesis.
39. Computed value > critical value: Reject the null hypothesis
40. z-computed = 1.130, critical value = 1.96: Fail to reject the null hypothesis
Population Proportion
41. Sample proportion of 90 out of 150 making a purchase: 0.60
42. Test statistic: -1.414
43. Test statistic: 0.426
44. Rejection region (one-tailed, right): z > 1.645
45. Rejection region (two-tailed): z < -2.575 or z > 2.575
46. -1.317
Hypothesis Testing Procedure
10. Rejection Region: The area in the normal curve that leads to rejection of the null hypothesis.
11. Degrees of Freedom: The number of values that are free to vary in a data set.
13. One-tailed Test
25. σ = 0.7
31. Last step in hypothesis testing: Draw a conclusion
38. First step in hypothesis testing: State the null and alternative hypotheses