# HW 6 - HW 6 Distribution Free Tests(two samples 1 Fill in...

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Unformatted text preview: HW 6 Distribution Free Tests (two samples) 1. Fill in the blank. In our class, we apply a non parametric test when we have a small data set that does not come from a normal population. In practice, for certain shaped distributions, we might try a ________________ first, which may allow us to apply a t based inference. 2. Suppose we have a dependent samples data set. Further suppose that the differences come from a normal distribution. True or False: The dependent samples t test is more powerful than the sign test. TRUE FALSE 3. Consider two samples of size n1 = 9 and n2 = 3. Use Table 6 to bracket the P‐value using a non‐directional alternative. a. Us = 21 b. Us = 24 c. Us = 25 d. Us = 28 4. 7.80. Recall the study described in exercise 7.51 on your previous homework. In this study of hypnosis, breathing patterns were observed in an experimental group of subjects and in a control group. The measurements of total ventilation (liters of air per minute per square meter of body area) are shown in the following table. Experimental Control 5.32 4.50 5.60 4.78 5.74 4.79 6.06 4.86 6.32 5.41 6.34 5.70 6.79 6.08 7.18 6.21 n8 Y 6.169 s 0.621 8 5.291 0.652 a. When you computed a confidence interval using this data on your last homework, you were told to proceed as though the assumptions for validity of a t based inference were checked and deemed acceptable. Use the QQplot to check the normality assumption. b. Conduct the appropriate test to see if ventilation tends to be higher in the "to be hypnotized" group. Operate at α = 0.05. 5. 9.53. For an investigation of the mechanism of wound healing, a biologist chose a paired design, using the left and right hindlimbs of the salamander Notophthalmus viridescens. After amputating each limb, she made a small wound in the skin and then kept the limb for 4 hours in either a solution containing benzamil or a control solution. She theorized that the benzamil would impair the healing. The accompanying table shows the amount of healing, expressed as the area (mm2) covered with new skin after 4 hours. Animal 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Control .55 .15 .00 .13 .26 .07 .20 .16 .03 .42 .49 .08 .32 .18 .35 .03 .24 Benzamil .14 .08 .00 .13 .10 .08 .11 .00 .05 .21 .11 .03 .14 .37 .25 .05 .16 a. Use the QQplot to check the assumption of normality. b. Use an appropriate hypothesis test to assess the significance of the researcher's hypothesis about the effect of Benzamil. Operate at the α = 0.05 significance level. 6. 7.84. Human beta‐endorphin (HBE) is a hormone secreted by the pituitary gland under conditions of stress. An exercise physiologist measured the resting (unstressed) blood concentration of HBE in two groups of men: Group 1 consisted of 11 men who had been jogging regularly for some time, and group 2 consisted of 15 men who had just entered a physical fitness program. (This data was from the same research study on HBE we used in your Inference for the Population Mean HW, exercise 6.16.) The results are given in the following table. Joggers 39 40 32 60 19 52 41 32 13 37 28 Fitness Program Entrants 70 47 54 27 31 42 37 41 9 18 33 23 49 59 41 a. Use the QQplot to check the assumption of normality for a t distribution based inference. b. Conduct the appropriate test to compare the two groups. Operate at the α = 0.05 significance level. c. Instead of a non‐directional alternative, suppose the researchers believed the HBE would tend to be higher for the joggers group. What would the P‐value be for this test? 7. 9.33. In an investigation of possible brain damage due to alcoholism, an X‐ray procedure known as a computerized tomography (CT) scan was used to measure brain densities in eleven chronic alcoholics. For each alcoholic, a nonalcoholic control was selected who matched the alcoholic on age, sex, education, and other factors. The brain density measurements on the alcoholics and the matched controls are reported in the accompanying table. Pair Alcoholic Control Difference 1 40.1 41.3 ‐1.2 2 38.5 40.2 ‐1.7 3 36.9 37.4 ‐0.5 4 41.4 46.1 ‐4.7 5 40.6 43.9 ‐3.3 6 42.3 41.9 0.4 7 37.2 39.9 ‐2.7 8 38.6 40.4 ‐1.8 9 38.5 38.6 ‐0.1 10 38.4 38.1 0.3 11 38.1 39.5 ‐1.4 a. Use the QQplot assess whether the normality assumption has been met. a. Use the appropriate test to test the null hypothesis of no difference against the alternative that alcoholism reduces brain density. Let α = 0.05. b. Suppose the researcher for this study only wanted to see if there was a significant difference in brain density (i.e. a non‐directional alternative). What would the P‐value be for this test? ...
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