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Section 9.4

Section 9.4. Day 3. Power. Power of a significance test is the probability of rejecting the null hypothesis. Power. Power of a significance test is the probability of rejecting the null hypothesis. Best way to get more power to reject a false null hypothesis is to _______ ____ ______.

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Section 9.4

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  1. Section 9.4 Day 3

  2. Power Power of a significance test is the probability of rejecting the null hypothesis.

  3. Power Power of a significance test is the probability of rejecting the null hypothesis. Best way to get more power to reject a false null hypothesis is to _______ ____ ______.

  4. Power Power of a significance test is the probability of rejecting the null hypothesis. Best way to get more power to reject a false null hypothesis is to increase sample sizes.

  5. Power If we have reason to believe the population standard deviations are about equal, make the sample sizes the same.

  6. Power If we have reason to believe the population standard deviations are about equal, make the sample sizes the same. If we have reason to believe that one population’s standard deviation is larger than the other’s, allocate our resources so you take a larger sample from the population with the larger standard deviation.

  7. Page 632, P31

  8. Power Which level has the greater spread?

  9. Page 632, P31 The previous data indicate that the measurements from the bottom of the river have a greater spread, so ….

  10. Page 632, P31 Because the previous data indicate that the measurements from the bottom of the river have a greater spread, getting more of the new measurements at the bottom of the river would give the test greater power.

  11. Page 636, E60

  12. Page 636, E60 What are the treatments here?

  13. Page 636, E60 What are the treatments here?

  14. Page 636, E60 What are the experimental units here?

  15. Page 636, E60 The experimental units are the panels, not the individual members. So, the size of each treatment group is 8 because 8 panels were assigned to each texture.

  16. Page 636, E60 Name:

  17. Page 636, E60 This is a two-sided significance test for the difference between two means. Question asked “Is there a statistically significant difference in mean palatability score between the two texture levels?”

  18. Page 636, E60 Check conditions:

  19. Page 636, E60 Check conditions: This is an experiment. Panel members were randomly assigned to the treatment groups as they were recruited.

  20. Page 636, E60 List 1: scores for coarse texture List 2: scores for fine texture

  21. Page 636, E60 Check conditions: Show your graphs.

  22. Page 636, E60 Check conditions: Looking at distribution of scores for each texture, both distributions are fairly symmetric with no outliers. It’s reasonable to assume each sample came from a normally distributed population.

  23. Page 636, E60 State hypotheses.

  24. Page 636, E60 State hypotheses.

  25. Page 636, E60 Compute test statistic, find P-value, and draw sketch.

  26. Page 636, E60 Compute test statistic, find P-value, and draw sketch. 2-SampTTest μ1: ≠ μ2 Inpt: Data Pooled: No List1: L1 Calculate List2: L2 Freq1: 1 Freq2: 1

  27. Page 636, E60 Compute test statistic, find P-value, and draw sketch. t ± 4.929 P-value 0.00022

  28. Page 636, E60 If all the panels sampled food with a coarse texture and all the panels sampled food with a fine texture, I would reject the null hypothesis because the P-value of 0.00022 is less than the significance level of 0.05.

  29. Page 636, E60 If all the panels sampled food with a coarse texture and all the panels sampled food with a fine texture, I would reject the null hypothesis because the P-value of 0.00022 is less than the significance level of 0.05. Thus, there is sufficient evidence to support the claim that there is a statistically significant difference in the mean palatability score between the coarse texture food and the fine texture food.

  30. Page 634, E58

  31. Page 634, E58 a) These are not independent random samples of men and women but an observational study conducted by looking at medical charts in one city.

  32. Page 634, E58 a) These are not independent random samples of men and women but an observational study conducted by looking at medical charts in one city. The data is fairly symmetrical so the underlying populations probably are approximately normal. There is one outlier for the males.

  33. Page 634, E58 a) The populations of men and women are larger than 10 times their sample sizes (respectively 10(91) = 910 and 10(84) = 840)

  34. Page 634, E58 Although conditions not met, we need to find the P-value for part b. Name of test we would use:

  35. Page 634, E58 Although conditions not met, we need to find the P-value for part b. Name of test we would use: One-sided significance test for the difference of two means It has been speculated that the mean amount of calcium in the blood is higher in women than in men.

  36. Page 634, E58 State hypotheses. Ho:

  37. Page 634, E58 State hypotheses. Ho: μf = μm, where μf and μm are the mean calcium levels in the blood of women and men, respectively.

  38. Page 634, E58 State hypotheses. Ho: μf = μm, where μf and μm are the mean calcium levels in the blood of women and men, respectively. Ha: μf > μm It has been speculated that the mean amount of calcium in the blood is higher in women than in men.

  39. E58 2-SampTTest Inpt: Stats μ1 > μ2 x1: 2.39690048 Pooled: No Sx1: 0.14049805 Calculate n1: 84 x2: 2.3181319 Sx2: 0.12172749 n2: 91

  40. E58 2-SampTTest Inpt: Stats μ1 > μ2 x1: 2.39690048 (F) Pooled: No Sx1: 0.14049805 stdDev Calculate n1: 84 x2: 2.3181319 (M) t = 3.94938702 Sx2: 0.12172749 p = 0.00005794 n2: 91

  41. Page 634, E58 t 3.95; P-value 0.00005 3.95

  42. Page 634, E58 Interpret P-value: If these could be considered independent random samples of men and women and if there was no difference between the mean calcium levels in the blood of men and women, the probability of a t-statistic of 3.95 or larger with samples of 84 women and 91 men is 0.00005.

  43. Page 634, E58 Interpret P-value: If these could be considered independent random samples of men and women and if there was no difference between the mean calcium levels in the blood of men and women, the probability of a t-statistic of 3.95 or larger with samples of 84 women and 91 men is 0.00005. However, because this was an observational study, these results are questionable.

  44. Page 632, E53

  45. Page 632, E53 a) The treatments, raised in long days or raised in short days, were randomly assigned to subjects.

  46. Page 632, E53

  47. Page 632, E53

  48. Page 632, E53 a) Both distributions are moderately skewed, but neither has any outliers. Since the distribution of the difference reduces skewness, and the t-procedure is robust against non-normality, the conditions for inference are adequately met to proceed.

  49. Page 632, E53 b. Interval?

  50. Page 632, E53 b. (0.50251, 9.46)

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