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Understanding Null and Alternative Hypothesis in Hypothesis Testing

This chapter covers hypothesis testing, a key statistical process to evaluate if a conjecture is valid. It explains the concepts of null and alternative hypotheses, Type I and II errors, and the distinction between one-tailed and two-tailed tests. The chapter guides readers through the steps for hypothesis testing, critical values, and p-value methods. Examples illustrate practical applications, ensuring clarity in differentiation between accepted or rejected hypotheses based on statistical evidence. This foundational knowledge is crucial for data analysis and decision-making.

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Understanding Null and Alternative Hypothesis in Hypothesis Testing

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  1. Chapter 8 Hypothesis Testing

  2. 8.2 Null and Alternative Hypothesis Hypothesis testing is the process we go through to decide whether or not the conjecture is true.

  3. 8.2 Test Value If the observed (sample) mean is a lot different than the hypothesized population mean, we conclude the hypothesized mean is incorrect.

  4. 8.2 Identifying Null and Alternative Hypothesis

  5. 8.2 Type I and II Errors

  6. 8.2 Type I and II Errors

  7. 8.2 Type I and II Errors

  8. 8.2 Two Tailed vs. One Tailed Test Bottom pg 394 has English to symbols translations.

  9. 8.2 One Tailed Test; α = .01 1 - .01 = .99 Look up .49, what value of z do you get? .5 - .01 = .49 2.33 Critical Value

  10. 8.2 One Tailed Test; α = .01 Right-Tail Test Left-Tail Test

  11. 8.2 Two Tail Test If α = .01

  12. 8.2 Critical Values α= .10,.05,.01

  13. 8.2 Example 1

  14. 8.2 Example 1

  15. 8.2 Example 1 .4901 2.33

  16. 8.3 z Test for a Mean

  17. 8.3 Steps for Hypothesis Testing

  18. 8.3 Example 2

  19. 8.3 Example 2

  20. 8.3 Example 3

  21. 8.3 Example 3

  22. 8.3 P-value Method for Hypothesis Testing

  23. 8.3 Example 4

  24. 8.3 Example 4

  25. 8.3 Example 5

  26. 8.3 Example 5

  27. 8.3 Decision Rules for P-Values If you are not given an α value: X X ? √ 0 .05 .10 .01

  28. 8.4 t Test for a Mean In chapter 7, when n <30 and σ was unknown we used tα/2 values verses z α/2 values for our confidence intervals.

  29. 8.4 Example 6

  30. 8.4 Example 7 Look at the One tail α heading Use the .01 column Go down to row 22 -2.508 Look at the Two tails α heading Use the .10 column Go down to row 18 -1.734 and +1.734

  31. 8.4 Example 8

  32. 8.4 Example 8

  33. 8.4 Example 9 d.f. = 11 – 1 = 10 Look in row 10 for t-value 2.056 (or the closest two values you can find. For the t-value up to the top of the column; use the One-tail heading.

  34. 8.4 Example 9

  35. 8.4 Example 9 .025 < p-value < .05 If we were testing at the α = .05 level would we accept or reject H0? Reject because p-value < .05

  36. 8.4 Example 10 Look in row 5 for t-value 2.983 Use the Two-tails heading .05 .02 2.571 2.983 3.365 .02 < p-value < .05 If α = .01 level would we accept or reject H0? Do not reject since p-value > .02 > .01

  37. 8.4 Example 10

  38. 8.4 Example 10

  39. 8.5 z-Test for Proportion

  40. 8.5 Example 11

  41. 8.5 Example 11

  42. 8.5 Example 11

  43. 8.5 Example 11

  44. 8.5 Example 11

  45. 8.5 Example 11

  46. 8.5 Example 12

  47. 8.5 Example 12

  48. 8.6 X2 Test for σ2 or σ • The areas for Chi-square distribution Table G pg 772 • Left, right and two tailed test • Chi-square distribution different than z and t in that the values are never negative

  49. 8.6 Example 13

  50. 8.6 Example 13

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