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SRM 603 Assignment 1 1. A rehabilitation center researcher was interested in examining the relationship between physical fitness prior to corrective knee surgery and time required in physical therapy until successful rehabilitation. Using patient records, 24 male subjects ranging in age from 18 to 30 years who had undergone similar corrective knee surgery during the past year were selected for the study. The number of days required for successful completion of physical therapy and the prior physical fitness status (below average, average, above average) for each patient are as follows. Below Average (1) 29 42 38 40 43 40 30 42 Average (2) 30 35 39 28 31 31 29 35 29 33 Above Average (3) 26 32 21 20 23 22 (a) Write an appropriate ANOVA model for this research question. (b) Specify the appropriate null and alternative hypotheses for this research question. (c) Use SAS to construct an ANOVA table, and perform a test of the hypotheses from part b using significance level α = 0.05. (d) Explain the result of the hypothesis test from part c in terms of the language of the original problem. (e) Use SAS to estimate the treatment effects, and explain these in terms of the language of the original problem. 2. Using the EXERCISE data set, create a new variable PUL GAIN which is the difference in the post-exercise ( PULSE 2) and pre-exercise pulse ( PULSE 1) rates, and compare the smokers and non smokers on this variable. Data are available in the text file “ EXERCISE.txt”. (a) Write an appropriate ANOVA model for this question. (b) Specify the appropriate null and alternative hypotheses for this research question. (c) Use SAS to construct an ANOVA table, and perform a test of the hypotheses from part b using significance level α = 0.05. (d) Explain the result of the hypothesis test from part c in terms of the language of the original problem. (e) Use SAS to estimate the treatment effects, and explain these in terms of the language of the original problem. (f) Compare the smokers and non smokers on PUL GAIN using a t-test. Compare the observed F−ratio with the observed t−ratio. 3. Researchers compared the amount of DDT in the breast milk of a random sample of 12 Hispanic women in Yakima Valley in Washington State with the amount of DDT in breast milk in the general U.S. population. They measured the standard deviation of the amount of DDT in the general population to be 36.5 parts per billion (ppb). Assume the population is normally distributed. We are interested in testing whether the population standard deviation of DDT level in the breast milk of Hispanic women in Yakima Valley is grater than that of the general population, using level of siginificance α = .01. (a) Specify appropriate null and alternate hypotheses. (b) The sample variance is s2 = 119, 025. Calculate χ2obs. (c) Calculate the p−value and compare it with α. State your conclusion. (d) Find the critical value and compare it with χ2obs. State your conclusion. (e) Construct a 95% confidence interval for the population variance. 4. “Do two types of music, type-I and type-II, have different effects upon the ability of college students to perform a series of mental tasks requiring concentration?” To verify this question a subject pool of college students, randomly were sorted into two groups, A and B. The members of each group performed a series of mental tasks under conditions that were identical in every respect except that group A had music of type-I playing in the background, while group B had music of type-II. The data were collected as follows: Group A Group B music of type-I music of type-II 26 21 22 18 23 21 26 19 22 20 20 29 26 25 24 20 16 20 21 23 23 26 21 25 18 29 22 17 18 19 Assume the normality of scores for both groups and test for equality of variances using α = .01. (a) State the null and alternate hypotheses, (b) report the value of the test statistic, (c) find the critical value, and (d) report your decision regarding the null hypothesis and your conclusion in the context of the problem. (e) Find a 95% CI for the ratio of variances. 5. Run a SAS program to verify your results from problem 4. 6. Use the HSB data set to test the HOV for the writing scores (WRTG) for the three socio-economic groups (SES), using the Bartlett test. Report (a) the value of the test statistic and its corresponding p-value, (b) specify the null and the alternate hypotheses that are being tested, and (c) clearly state the conclusion of the test in the context of the problem ( you may use α = .05). 7. Using the EXERCISE data set, create a new variable PUL GAIN which is the difference in the post-exercise ( PULSE 2) and pre-exercise pulse ( PULSE 1) rates and compare the variability of smokers and non smokers on this variable. (a) Specify the appropriate null and alternative hypotheses for this question. (b) Use SAS to perform a test of the hypotheses from part a using significance level α = 0.05. (c) Explain the result of the hypothesis test from part b in terms of the language of the original problem. (d) Set the 90% CI for the ratio of the variances.