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- QUESTION 12 Historically, the proportion of people who trade in their old car to a car dealer when purchasing a new car is 48%. Over the previous 6 months, in a sample of 115 new-car buyers, 46 have traded in their old car. To determine (at the 10% level of significance) whether the proportion of new-car buyers that trade in their old car has statistically significantly decreased, what can you conclude concerning the null hypothesis? Reject the null hypothesis Fail to reject the null hypothesisSuppose Xn is an IID Gaussian process, withµX[n]=1, and σ2 X[n]=1Now, another stochastic process Yn = Xn − Xn−1. Please find:(a) The mean µY (n).(b) The variance σ2Y (n).(c) The auto-correlation RY (n, k)Question 16Serial correlation in the residuals of a time series regression can occur if you fail toinclude a relevant lag of the dependent variable as an explanatory variable in the regression. O TrueO False
- QUESTION 12 Historically, the proportion of people who trade in their old car to a car dealer when purchasing a new car is 48%. Over the previous 6 months, in a sample of 115 new-car buyers, 46 have traded in their old car. To determine (at the 10% level of significance) whether the proportion of new-car buyers that trade in their old car has statistically significantly decreased, what can you conclude concerning the null hypothesis?Stock y has a beta of 1.2 and an expected return of 11.5. Stock z has a beta of .80 and an expected return of 8.5 percentQuestion 8:Research at the University of Toledo indicates that 50% of students change their major area of study after their first year in a program. A random sample of 100 students in the College of Business revealed that 48 had changed their major area of study after their first year of the program. Has there been a significant decrease in the proportion of students who change their major after the first year in this program? Test at the .05 level of significance.
- 27. An article in Radio Engineering and Electronic Physics (1980, Vol. 25, pp. 74-79) investigated the behavior of a stochastic generator in the presence of external noise. The number of periods was measured in a sample of 100 trains for each of two different levels of noise voltage, 100 and 150 mV. For 100 mV, the mean number of periods in a train was 7.9 with s1 = 2.6. For 150 mV, the mean was 6.9 with s2 = 2.4. Use α = 0.01 and assume that each population is normally distributed and the two population variances are equal. (a) It was originally suspected that raising noise voltage would reduce mean number of periods. Do the data support this claim? (b) Calculate a confidence interval to answer the question in part (a).Question 2: Assume that the risk-free rate, RF, is currently 8%, the market return, RM, is 12%, and asset A has a beta, of 1.10. (could be done on word document or excel). Assume that as a result of recent events, investors have become more risk averse, causing the market return to rise by 2%, to be14%. Ignoring the shift in part c, draw the new SML on the same set of axes that you used before, and calculate and show the new required return for asset A. From the previous changes, what conclusions can be drawn about the impact of (1) decreased inflationary expectations and (2) increased risk aversion on the required returns of risky assets?: We assume that the stochastic process for a stock price is an Arithmetic Brownian motion, with a drift of 53% and, diffusion of 33%. Find the probability that the stock price will be between 0.78 and 1.25 in 4 years. (A) 0.06 (B) 0.04 (C) 0.08 (D) 0.05 (E) 0.07
- The price of a stock is modeled with a geometric Brownian motion with drift μ=-0.25 and volatility σ=0.4. The stock currently sells for $35. What is the probability that the price will be at least $40 in 1 year?If X1, X2, ... , Xn constitute a random sample of size n from an exponential population, show that X is a consis-tent estimator of the parameter θ.Question 4 Multi-Server QueueA supermarket manager is trying to decide how many cashers to employ for the peak time. The service times for check outs are exponentially distributed with a mean service time of 3 minutes. Customer arrivals to cashiers follow a Poisson arrival process with an average 110 customers per hour.a. What is the minimum number of cashers that would be needed to have the utilization less than one?b. If the waiting time is too long, customers might leave the store or even do not enter the store. It is estimated that for every minute of waiting time, the supermarket loses a potential profit of 50 HKD every hour from lost sales. The hourly wage for a casher is 80 HKD / hour. How many cashers should the supermarket employ to maximize its profit? (Keep four decimal places.