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- Consider a regression analysis with n = 47 and three potential independent variables. Suppose that one of the independent variables has a correlation of 0.95 with the dependent variable. Does this imply that this independent variable will have a very large Student’s t statistic in the regression analysis with all three predictor variables?Data was collected from 60 students from the SAT, the average sat score was 909 with a standard deviation of 178. The average ACT score was 19 with a standard deviation of 3.5. The correlation between the two variables is 0.811. a) To predict the SAT score from the ACT score, what is the equation of the leasts-square regression line. b) What fraction of the variation in the values of the SAT scores is accounted for by the linear relationship between SAT and ACT scores. ExplainA random sample of 20 newly-born baby boys showed an average weight of 7.40 pounds while a sample of 25 newly-born baby girls showed a mean weight of 6.50 pounds. If the variance of all newly-born babies are 1.25 pounds, can we say that newly-born baby boys are heavier than newly-born baby girls using the 0.05 level?
- The following data relate to marks in Advanced Accounts and Business Statistics in B.Com. (H.), Il yr Examination of a particular year in Delhi University : Mean Marks in Advanced Accounts Mean Marks in Business Statistics Standard Deviation of Marks in Advanced Accounts Standard Deviation of Marks in Business Statistics Coefficient of Correlation between the Marks in Advanced Accounts and Business Statistics Find the two regression lines and calculate the expected marks in Advanced Accounts if the marks secured by a student in Business Statistics are 40. = 30 = 35 = 10 = 7 = 0-83) For a sample of 306 students in a basic business communications course, the sample regression line y = 58.813 + 0.2875x was obtained. Here y = final student score at the end of the course x = score on a diagnostic writing skills test given at the beginning of the course The coefficient of determination was 0.1158 and the estimated standard deviation of the estimator of the slope of population regression line was 0.04566. a) Define and interpret the estimates of the regression equation. b) Interpret the coefficient of determination. c) What will happen to the final student score if his diagnostic writing test score increases by 2? d) How can you inmprove this model?4. To assess the effect of state right to work laws on union membership (which do not require membership in unions as a precondition for employment), the following regression results were obtained from the data for 50 states in the United States for 1982: PVT, = 19.8066 – 9.3917 RTW, t= (17.0352) (-5.1086) R = 0.3522 where PVT = percentage of private sector employees in unions in 1982 RTW = 1 if right-to-work law exists, 0 otherwise (in 1982, 20 states had right- to-work laws). %3D A priori, what is the expected relationship between PVT and RTW? Do the regression results support this expected relationship? Interpret the regression results. What was the average percent of private sector employees in unions in the states that did not have the right-to-work laws?
- One study claims that the variance in the resting heart rates of smokers is different than the variance in the resting heart rates of nonsmokers. A medical student decides to test this claim. The sample variance of resting heart rates, measured in beats per minute, for a random sample of 9 smokers is 480.7. The sample variance for a random sample of 9 nonsmokers is 131.6. Assume that both population distributions are approximately normal and test the study’s claim using a 0.10 level of significance. Does the evidence support the study’s claim? Let smokers be Population 1 and let nonsmokers be Population 2. Step 1 of 3: State the null and alternative hypotheses for the test. Fill in the blank below. H0: σ21=σ22: Ha: σ21⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯σ22 Step 2 of 3: Compute the value of the test statistic. Round your answer to four decimal places. Step 3 of 3: Draw a conclusion and interpret the decision.Given that the means of x and y are 64 and 66 , their standard deviations are 2.8 and 3.2 respectively and the coefficient of correlation between them is 0.5. 1) write down the regression lines.A professor claims that the final exam grades are more widely dispersed in Principles classes compared to upper-level classes. In a sample of 101 Principles final exams, the standard deviation is 16 while in a sample of 30 upper-level class final exams the standard deviation is 13. Test the hypothesis at the 10% level of significance that the 2 variances are different. Write all formulas and hypothesis.
- 2. The average zone of inhibition (in mm) for mouthwash L as tested by the medical technology students has been known to be 9mm. A random sample of 10 mouthwash L was tested and the test yielded an average zone of inhibition of 7.5mm with a variance of 25 mm. Is there enough reason to believe that the anti-bacterial property of the mouthwash has decreased? Test the hypothesis that the average zone of inhibition of the mouthwash is no less than 9mm using 0.05 level of significance. A. State the hypotheses. B. Determine the test statistic to use. C. Determine the level of significance, critical value, and the decision rule. D. Compute the value of the test statistic. E. Make a decision. F. Draw a conclusion.The sales manager of a large company selected a random sample of n = 10 salespeople and determined for each one the values of x = years of sales experience and y = annual sales (in thousands of dollars). A scatterplot of the resulting (x, y)pairs showed a linear pattern.(a)Suppose that the sample correlation coefficient is r = 0.75 and that the average annual sales is y = 100.If a particular salesperson is 2 standard deviations above the mean in terms of experience, what would you predict for that person's annual sales?Since the value for experience is 2 standard deviations above the mean experience, you can predict annual sales will be ________________standard deviations above the mean annual sales.(b)If a particular person whose sales experience is 1.7 standard deviations below the average experience is predicted to have an annual sales value that is 1 standard deviation below the average annual sales, what is the value of r? (Round your answer to two decimal places.)r =Calculate estimates of the standard deviations sz, Sy of the samples r = (5,9, 7) and y = (-1,2,5) as well as the Pearson coefficient of correlation rry of r and y. Which of the following answers are correct? a) sz = 4, sy = 9 b) rzy = 0 c) sz = 2, sy = 3 d) Tzy = } e) rzy =