5. Imagine that I have a therapy that I believe will lower people's anxiety. Using the following measurement of people's anxiety after having had a course of the therapy, conduct a two- tailed z-test against the null hypothesis that the u = 55 and o = 6. 47 54 39 43 53 45 47 49 46 38 58 44 43 45 50 51 52 52 46 42 Be sure to include in your answer a histogram of the data, the mean and sd of the data, formal statements of the null and alternative hypotheses, the critical value of z, the observed value of z, a statement of the statistical result, and an English-language statement of you conclusion. 6. Imagine that I have a training system that I believe will raise children's school grades (out of 100). I do not know the population parameters for school grades, however. So, I check my participants' grades prior to training them, and then again after training. My data are as follows: Student#: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Before: 55 71 80 64 71 92 78 65 54 63 66 60 63 85 89 70 57 72 73 69 After: 76 67 65 85 71 67 89 75 93 68 73 82 80 76 76 68 85 85 77 78 Conduct the appropriate two-tailed test to see if there is a difference in grades before and after training. Be sure to include in your answer the mean and standard deviation of the differences, formal statements of the null and alternative hypotheses, the critical value of the test statistic, the observed value of the test statistic, a statement of the statistical result, and an English- language statement of you conclusion. 7. | theorize that drug addiction is caused by the symptoms of withdrawal from the drug, but that the intensity of the withdrawal symptoms is strongest when the animal remains in the environment where it has been habitually exposed to the drug. By moving the animal to a new environment, I should be able to reduce the withdrawal symptoms to the point that the addiction ends. To test this hypothesis, | repeatedly exposed two groups of rats to a drug that is known to be addictive. Then, I left one group of addicted rats in the same environment where they received the drug, and | shifted the other group to a different environment. Neither group was given more of the drug, which allowed withdrawal symptoms to develop. I measured the rats' movements over an hour (where more movement indicates "agitation,\" a common symptom of drug withdrawal). My data are as follows. Same: 21 15 25 29 30 41 35 15 1'7 30 31 33 49 25 26 27 20 18 31 26 Diff: 16 21 2O 15 24 25 17 23 22 16 18 26 16 10 20 20 22 33 29 29 32 19 24 2? Conduct the appropriate two-tailed test to see if there is a difference in the amount of movement in the two groups of rats. Be sure to include in your answer the means and standard deviations of the groups, formal statements of the null and alternative hypotheses, the critical value of the test statistic, the observed value of the test statistic, a statement of the statistical result, and an English-language statement of you conclusion. Finally, include a measure of the effect size