#9 1. A sample is selected from a population with = 50. After a treatment is administered to the individuals in the sample, the mean is found to be M = 55 and the variance is s 2 = 64. a. If the sample has n = 4 scores, then conduct a hypothesis test to evaluate the significance of the treatment effect. Use a two-tailed test with = .05. b. If the sample has n = 16 scores, then conduct a hypothesis test to evaluate the significance of the treatment effect. Use a two-tailed test with = .05. c. Describe how increasing the size of the sample affects the likelihood of rejecting the null hypothesis and the measure of effect size. 2. A researcher would like to evaluate the effect of a new cold medication on reaction time. It is known that under regular circumstances the distribution of the reaction times is normal with = 200. A sample of n = 9 participants is obtained. Each person is given the new cold medication and 1 hour later reaction time is measured for each individual. The average reaction time for this sample M= 206 with SS=648. a. Use the two-tailed test with the alpha level a=0.05 to determine whether the medication has a significant effect on reaction time. b. Use the one-tailed test with the alpha level a =0.01 to determine whether the medication produces a significant increase on reaction time. 3. A sample of n =16 individuals is selected from a population with a mean of =80. A treatment is administered to the sample, and after the treatment, the sample mean is found to be M= 86 with a standard deviation of s = 8. a. Does the sample provide sufficient evidence to conclude that the treatment has a significant effect? Test with a=0.05. b. Now assume the sample has only n=4 individuals, but the mean and standard deviation are still the same. Repeat the hypothesis test with a=0.05. c. Finally, assume the standard deviation for the original sample (n=16) was increased to 12. Once again, repeat the hypothesis test with a=0.05. 4. A psychologist would like to determine whether there is a relation between depression and aging. It is known that the general population averages = 40 on a standardized depression test. The psychologist obtains a sample of n = 9 individuals who are all older than the age of 70. The depression scores are 37, 50, 43, 41, 39, 45, 49, 44, 48. On the basis of this sample, can the psychologist conclude that depression for elderly people is significantly different from depression in the general population? Use a two-tailed test at the .05 level of significance