 # Quant Help

A pitching machine is calibrated to deliver a fastball at a speed of 98 miles per hour. Every day, a technician samples the speed of twenty-five fastballs in order to determine if the machine needs adjustment. Today, the sample showed a mean speed of 99 miles per hour with a standard deviation of 1.75 miles per hour. At a 95% confidence level, what is the z-value in relation to the critical value? A) The critical value exceeds the z-value by 1.3 standard deviations. B) The z-value exceeds the critical value by 1.5 standard deviations. C) The z-value exceeds the critical value by 0.9 standard deviations. D) The critical value exceeds the z-value by 0.7 standard deviations If the threshold return is higher than the risk-free rate, what will be the relationship between Roys safety-first ratio (SF) and Sharpes ratio? A) The SF ratio will be higher. B) The SF ratio will be lower. C) They will be the same. D) The SF ratio may be higher or lower depending on the standard deviation. Maria Huffman is the Vice President of Human Resources for a large regional car rental company. Last year, she hired Graham Brickley as Manager of Employee Retention. Part of the compensation package was the chance to earn one of the following two bonuses: if Brickley can reduce turnover to less than 30%, he will receive a 25% bonus. If he can reduce turnover to less than 25%, he will receive a 50% bonus (using a significance level of 10%). The population of turnover rates is normally distributed. The population standard deviation of turnover rates is 1.5%. A recent sample of 100 branch offices resulted in an average turnover rate of 24.2%. Which of the following statements is most accurate? A) Brickley should not receive either bonus. B) For the 25% bonus level, the test statistic is -10.66. C) For the 50% bonus level, the critical value is -1.65 and Huffman should give Brickley a 50% bonus. D) For the 50% bonus level, the test statistic is -5.33 and Huffman should give Brickley a 50% bonus. Please walkthrough and advise.

for prob 2 - as far i remember there were 2 formulaes - SF Ratio = (X (bar) - RFR) / s Sharpes ratio = (X (bar) - RL) / s Not sure to remember them correctly though. So if RL> RFR then -->> SF ratio should be higher. Just recheck my forumlae and you can get the answer right. The other 2 are a little difficult for me, I did not conc. much on the t-stat, z-stat cal. for June.

A pitching machine is calibrated to deliver a fastball at a speed of 98 miles per hour. Every day, a technician samples the speed of twenty-five fastballs in order to determine if the machine needs adjustment. Today, the sample showed a mean speed of 99 miles per hour with a standard deviation of 1.75 miles per hour. At a 95% confidence level, what is the z-value in relation to the critical value? A) The critical value exceeds the z-value by 1.3 standard deviations. B) The z-value exceeds the critical value by 1.5 standard deviations. C) The z-value exceeds the critical value by 0.9 standard deviations. D) The critical value exceeds the z-value by 0.7 standard deviations z-value = z-calc = (99-98)/(1.75/sqrt(25)) = 1/.35 = 2.857 95% critical value = t 0.025, 24 = 2.064 so z-value exceed crit - A and D are out. 2.9 - 2 approx 0.9. So Choice C If the threshold return is higher than the risk-free rate, what will be the relationship between Roys safety-first ratio (SF) and Sharpes ratio? A) The SF ratio will be higher. B) The SF ratio will be lower. C) They will be the same. D) The SF ratio may be higher or lower depending on the standard deviation. Safety First = Rm - Threshold / Std Dev Sharpe = Rm - rf / Std Dev Since Threshold return > rf --> Rm - Threshold < Rm - rf lets take numbers Rm = 10 rf = 6 threshold = 8, std dev = 2 sharpe = 4/2 = 2, safety first = 2/2 = 1 so SF ratio will be lower. Choice B Maria Huffman is the Vice President of Human Resources for a large regional car rental company. Last year, she hired Graham Brickley as Manager of Employee Retention. Part of the compensation package was the chance to earn one of the following two bonuses: if Brickley can reduce turnover to less than 30%, he will receive a 25% bonus. If he can reduce turnover to less than 25%, he will receive a 50% bonus (using a significance level of 10%). The population of turnover rates is normally distributed. The population standard deviation of turnover rates is 1.5%. A recent sample of 100 branch offices resulted in an average turnover rate of 24.2%. Which of the following statements is most accurate? A) Brickley should not receive either bonus. B) For the 25% bonus level, the test statistic is -10.66. C) For the 50% bonus level, the critical value is -1.65 and Huffman should give Brickley a 50% bonus. D) For the 50% bonus level, the test statistic is -5.33 and Huffman should give Brickley a 50% bonus. two ratios to compare For the 50% bonus 24.2 - 25 / (1.5 /sqrt(100)) = -0.8 / .15 = -5.33 For the 25% bonus 24.2 - 30 / (1.5 / sqrt(100)) = -5.8 / .15 = -38.66 A is wrong (at least a 25% bonus is forthcoming). z-crit = z with 10 percent on 1 tail = -1.283

1. is A. 99-98/1.75/5=2.85, critical value is 1.96; therefore, the difference is 0.89 and the answer is C. 2) B, will be lower, becuase for roy safety you substract threshold from return/std and sharp ration you substract RFR/from return/std, since threshold is higher than RFR, then it will be lower. 3) the only correct answer in there is D. I calculated t-test: 24.2-30/1.5/square root of 100= -30.66 and for 25% = -5.33

Ok … my formulaes were the other way round. I have forgotten most of the formulae stuff… hhhuf.