| (6 pts] Suppose you have some money to invest for simplicity ,81and are planning to put a fraction W into a stock market mutual fund and the rest [1 W}, into a bond mutual fund .Suppose that a $1 invested in a stock fund yields Roafter one year and a $1 invested in a bond fund yields Rb. R0 and Rb are random variables with expected value of 9% and 6% respectively ,and standard deviation of 5% and 3% respectively The correlation between RD and Rh is 0.?0 . If you place a fraction W ofyour m oney in the stock fund and the rest {1 W}, in the bond fund then the return on your investment will be R = WR +{1 w)Rb . The risk associated with your investment is measured by the standard deviation a. If you decide to invest 60% of your $11 in stock and the rest in bond , then what is the expected return of your investment ? What is its associated risk ? [2pts } b. What share of your $1 money should you invest in bond in order to expect a 8% return on your investment? For that same share i.e. invested in stock, what level of risk is associated with your investment ? (Zpts } c. What share of your 51 money should you invest in stock mutual fund in order for your investment risk to be 4%? [you can show your work using algebra ,or calculus ]. l2pts} II[ir' pts} A city wants to know if a new advertising campaign to make citizens aware of the dangers of driving after drinking has been effective .They count the number of drivers who have been stopped with more alcohol in their systems than the law allows for each day of the week in the week before and the week a month after the campaign starts . Let D:be the difference between the number of drivers caught with excessive alcohol in their systems before and after the campaign on each calendar day in any given week .Treat these as a random sample from a Normal (.11., 0'\") distribution Information collected randomly during the seven days of a week before and a week a month after the campaign , indicate a mean difference d = -2 , and a standard deviation 5 = 3.162 . a. Obtain a 95% confidence intervalfor the true average difference in num ber of drivers stopped with excess alcohol in their systems .[1ptl b. You are asked by the city administration to study whether the advertising campaign has been effective .State in terms of JLi,the relevant null and alternative hypothesis in conducting this study . [lptl c. Compute the tstatistic for testing H:against H: [lptl d. Obtain the p value for the test [lptl e. Do you reject H:at the 5% level ? At the 1% level ? (lpt } f. Provide a short summary of your conclusions from this study .Comment on the practical versus statistical significance of this estimate .[2pts]
