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Practice Exam 1 Public Health 6415 1. The value of diet, exercise and meditation was studied in 16 hypertensive women. The researchers believe these women will observe a change in their diastolic blood pressure after 4 months in the experimental program. The pretrial mean diastolic blood pressure of study participants is 120 mm Hg; their post-trial diastolic pressure is 115. Assume normality of the relevant distributions. Is there a difference in the mean diastolic blood pressure? Use = 0.05 , assume the standard deviation of the sample difference of before to after to be s=8. 1 2. Two brands of cigarettes are selected, and their nicotine content is compared. The data are shown here. Test the hypothesis that the means are different using =0.01. State your null and alternative hypotheses, size of the test, test statistic and value, p-value and conclusion. Assume all relevant distributions are approximately normal. (Hint: can you assume 1=2?) Brand A Mean = 28.6 milligrams s = 5.1 milligrams n=35 Brand B Mean = 32.9 milligrams s=4.4 milligrams n=27 2 3. A researcher wishes to try three different techniques to lower the blood pressure of individuals diagnosed with high blood pressure. The subjects are randomly assigned to three groups; the first group takes medication, the second group exercises, and the third group follows a special diet. After four weeks, the reduction in each person’s blood pressure is recorded. At =0.05, test the claim that there is no difference among the means. Use the SAS output below to help you test this hypothesis. ANOVA for Blood Pressure Change 1 11:00 Friday, February 10, 2006 The ANOVA Procedure Class Level Information Class Levels group 3 Values d e m Number of Observations Read Number of Observations Used 15 15 Anova for Blood Pressure Change 2 11:00 Friday, February 10, 2006 The ANOVA Procedure Dependent Variable: change Source DF Sum of Squares Mean Square F Value Pr > F Model 2 160.1333333 80.0666667 9.17 0.0038 Error 12 104.8000000 8.7333333 Corrected Total 14 264.9333333 R-Square Coeff Var Root MSE change Mean 0.604429 38.21407 2.955221 7.733333 Source DF Anova SS Mean Square F Value Pr > F group 2 160.1333333 80.0666667 9.17 0.0038 Anova for Blood Pressure Change 11:00 Friday, February 10, 2006 The ANOVA Procedure Level of group N ------------change----------Mean Std Dev 3 d e m 5 5 5 7.6000000 3.8000000 11.8000000 3.20936131 3.19374388 2.38746728 Hypothesis test: State your null and alternative hypotheses, test statistic, pvalue and conclusion. More on question 3: a. How many degrees of freedom are there for sum of squares between? b. What is the value of the mean of squares between? What does it represent? c. How many degrees of freedom are there for the sum of squares within? d. What is the value of the mean of squares within? What does it represent? e. Can we conclude there is a difference between the diet and exercise group? 4. Transient hypothyroxinemia, a common finding in premature infants, is not thought to have long-term consequences, or to require treatment. A study was performed to investigate whether hypothyroxinemia in premature infants is a cause of subsequent motor and cognitive abnormalities. Blood thyroxine values were obtained on routine screening in the first week of life from 536 infants who weighed 2000g or less at birth and were born at 33 weeks gestation or earlier. The data that follows were presented concerning the relationship between mean thyroxine level and gestational age. 4 Gestational Age (x) <24 25 26 27 28 29 30 31 32 33 Mean Thyroxide Level ug/dL (y) 6.5 7.1 7.0 7.1 7.2 7.1 8.1 8.7 9.5 10.1 These data were analyzed using SAS. The output follows. Use this output to answer questions. The REG Procedure Dependent Variable: thy Number of Observations Read Number of Observations Used 10 10 Analysis of Variance 5 DF Sum of Squares Mean Square 1 8 9 11.12836 2.09564 13.22400 11.12836 0.26195 Root MSE Dependent Mean Coeff Var 0.51181 7.84000 6.52825 Source Model Error Corrected Total R-Square Adj R-Sq F Value Pr > F 42.48 0.0002 0.8415 0.8217 Parameter Estimates Variable DF Parameter Estimate Standard Error t Value Pr > |t| Intercept age 1 1 -2.62727 0.36727 1.61408 0.05635 -1.63 6.52 0.1422 0.0002 95% Confidence Limits -6.34935 0.23733 1.09480 0.49721 6 A. Which is the dependent variable? Which is the independent variable? B. What is the equation for the least squares regression line for this data? C. Does there appear to be a linear association between mean thyroxine level and gestational age? Use the correlation to answer this question. If so, what is the strength and direction of this association? D. Test the null hypothesis that the correlation is zero vs. it is not zero. E. How much of the variation in mean thyroxine level is explained by the regression line of mean thyroxine level on gestational age? F. There were originally 536 infants in the study but we only have 10 observation points. G. Do you think the regression line for the original data or the 10 observations has a larger RSquare value? H. What is the expected mean value of thyroxine level for a baby whose gestational age is 27 weeks? Why? 7 I. What is the expected mean value of thyroxine level for a baby whose gestational age is 40 weeks? 8