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- A dietitian wishes to see if a person’s cholesterol level will be changed if the diet is supplemented by a certain mineral. Four subjects were pre-tested, and they took the mineral supplement for a 6-week period. The results are shown in the table. Is there sufficient evidence to conclude that the population mean of cholesterol levels has been changed after six weeks at α=0.2α=0.2? Assume that the differences are from an approximately normally distributed population. Subject Cholestrol Level (mg/dl) Cholestrol Level after 6 Weeks (mg/dl) dd ¯dd¯ (d−¯d)2(d-d¯)2 1 206 217 11 2 219 184 -35 3 202 204 2 4 213 205 -8 Total -30 a) Calculate the mean, the sum of the squared deviation from the mean, and the standard deviation of differences. Do not include the unit for each answer: ¯d=d¯= (do not round) ∑(d−¯d)2=∑(d-d¯)2= (do not round) sd=sd= (rounded to one decimal place) b) Perform the hypothesis test in the following steps: Step 1.…In Table 11.2 the estimated coefficient on black is 0.084 in column (1),0.688 in column (2), and 0.389 in column (3). In spite of these large differences, all three models yield similar estimates of the marginal effect of race on the probability of mortgage denial. How can this be?If the value of Cronbach’s alpha is 0.07, it means ___________; a. Research instrument is not reliable b. Research instrument is internally consistent c. Data is reliable d. Data is internally consistent
- Consider a capital market with only two risky assets A and B. Their standard deviations are 1 and 2, respectively. There is no risk-free asset. When the correlation coefficient ρAB = 0, construct a portfolio, whose variance is strictly less than 1. [Hint: you may want to try the portfolio that puts more weight on the security with the lower standard deviation.]Suppose that the index model for two Canadian stocks HD and ML is estimated with the following results: RHD =-0.03+2.10RM+eHD R-squared =0.7 RML =0.06+1.60RM+eML R-squared =0.6 σM =0.15 where M is S&P/TSX Comp Index and RX is the excess return of stock X. What is the covariance and the correlation coefficient between HD and ML? For portfolio P with investment proportion of 0.4 in HD and 0.6 in ML, calculate the systematic risk, non-systematic risk, and total risk of P.A possible important environmental determinant of lung function in children is the amount of cigarette smoking in the home. Suppose this question is studied by selecting two groups: Group 1 consists of 23 nonsmoking children 5-9 years of age, both of whose parents smoke, who have a mean forced expiratory volume (FEV) of 2.1 L and a standard deviation of 0.7 L; group 2 consists of 20 nonsmoking children of comparable age, neither of whose parents smoke, who have a mean FEV of 2.3 L and a standard deviation of 0.4 L.*8.31 What are the appropriate null and alternative hypotheses to compare the means of the two groups? *8.32 What is the appropriate test procedure for the hypotheses in Problem 8.31? *8.33 Carry out the test in Problem 8.32 using the criticalvalue method. *8.34 Provide a 95% CI for the true mean difference in FEV between 5- to 9-year-old children whose parents smoke and comparable children whose parents do not smoke. *8.35 Assuming this is regarded as a pilot study, how many…
- The director of marketing at Vanguard Corporation believes that sales of the company's Bright Side laundry detergent (S) are related to Vanguard's own advertising expenditures (A), as well as the combined advertising expenditures of its three biggest rival detergents (R).The marketing director collects 36 weekly observations on S, A, and R . Vanguard's marketing director is comfortable using parameter estimates that are statistically significant at the 10 percent level or better. Give the specific statistical tool that can be used to this problem.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?Consider a cohort study to compare the mortality rate of myocardial infarction (MI) in men with sedentary work (exposed group) to men with physically active work (unexposed). If in the exposed, there were 36,000 person (man) years of observation and 126 deaths whereas the unexposed had 24,000 man-years of observation and 44 deaths. Compute the following a) Mortality rate in each cohort? b) What is the relative risk of dying, comparing these 2 groups? c) What is the attributable risk of sedentary work? d) What is the attributable benefit of physical activity? e) If we assume that MI is associated with the mortality in this cohort (causality), what proportion of the disease in the higher group is potentially preventable?
- Suppose that the index model for two Canadian stocks HD and ML is estimated with the following results: RHD =-0.03+2.10RM+eHD R-squared =0.7 RML =0.06+1.60RM+eML R-squared =0.6 σM =0.15 where M is S&P/TSX Comp Index and RX is the excess return of stock X. What is the covariance and the correlation coefficient between HD and ML?The researchers reported:" A 2x2 ANOVA revealed, first of all, a main effect for depletion, indicating that depleted individuals generated less ideas (M = 9.40, SD = 5.64) than non-depleted individuals (M = 12.44, SD = 7.34), F (1, 108) = 6.03, p = .016, n2 = .05. This effect was qualified by the expected interaction with [perseverance], F (1,108) = 4.52, p = .036, n2 = .05". What size are the effects for the main effect of depletion and for the interaction between depletion and perseverance, according to Cohen's conventions? a. These are small- to -medium effects b. These are non existent effects c. These are large effects d. We are unable to tell from from the n2 / r2 statisticsThe management of a supermarket wants to adopt a new promotional policy of giving free gift to every customer who spends more than a certain amount per visit at this supermarket. The expectation of the management is that after this promotional policy is advertised, the expenditure for all customers at this supermarket will be normally distributed with mean 400 L.E and a variance of 900 L.E2. 1) If the management wants to give free gifts to at most 12% of the customers, what should the amount of expenditure be above which a customer would receive a free gift? 2) In a sample of 100 customers, what is the number of customers whose expenditure is between 420 L.E and 485 L.E? 3) What is a probability of selecting a customer whose expenditure is differ than the population mean expenditure by at most 50 L.E? 4) What is the percentage of customers whose expenditure is at least 450 L.E.?