QUESTION 17, CONTINUED:Proposed advertising 50 35 42 19 54 = 40 sd = 13.84| Skipped after Didn’t | TotalSkipped before | 50 70 | 120DS350 – QUANTITATIVE METHODS FOR BUSINESS DECISIONSFALL SEMESTER 2003“Ultimate Knowledge Festival”(known to the Mundane as the “Final Exam”)Answer the following questions in the space provided. SHOW YOUR WORK when appropriate.Relative problem weights are given in brackets; these total 100 points. Unless the problem statesotherwise, use the traditional confidence level of 95% and the traditional significance level of=.05.The word “pledged” in front of your signature on this exam is a sign of your ongoingcommitment to academic integrity and the Stetson University’s Honor System. ENJOY!!Question 1 [2 points]:Alphonso Ferrabosco II is conducting a hypothesis test to determine whether people can distinguish coffee from used motor oil, in a blind taste test. He obtains a p-value of .42. What statistical conclusion should he draw?_____ reject the null hypothesis _____ not reject the null hypothesis_____ reject the alternative hypothesis _____ not reject the alternative hypothesisQuestion 2 [2 points]:Continuing the example from Question 1, how should Alphonso phrase his conclusion, inthe context of the problem?_____ There is enough evidence to believe people can tell coffee from used motor oil._____ There is not enough evidence to believe people can tell coffee from used motor oil._____ There is enough evidence to believe people cannot tell coffee from used motor oil._____ There is not enough evidence to believe people cannot tell coffee from used motor oil.Question 3 [2 points]:Euterpe Waldfogel believes her pet wombat, Muffy, can successfully pick stocks. (Muffycan’t throw darts. Instead, selections are made by performing a biological function on pages of the Wall Street Journal.) Euterpe tests whether Muffy’s selections outperform the S&P 500. Sheobtains a p-value of .042 for her test. Which of the following is the best interpretation of this number?_____ Muffy’s picks outperformed the S&P 500 by 4.2%_____ There’s only a 4.2% chance that Muffy is actually able to pick stocks successfully._____ There’s only a 4.2% chance that the null hypothesis is true._____ Muffy selects good stocks 4.2% of the time._____ Stock selections as good as the ones Muffy made would happen by chance only 4.2% of the time.Question 4 [2 points]:Wilhelmine Tempusfugit is investigating the extent to which presidential elections are influenced by the economy. She has developed a regression model relating the percentage of vote obtained by the incumbent party (Y) to the percentage change of the Dow Jones Industrial Average in the six months preceding the election (X). Which of the following is the best quantity for Wilhelmine to examine, to see whether she has a statistically significant result?_____ Is the slope of the regression line positive? _____ Is the error variance (se2) small?_____ Is the coefficient of determination (r2) large? _____ Is the t-statistic for the slope large?Question 5 [2 points]:Gracetta Squornshellous wants to use double exponential smoothing on a data set consisting of 846 weeks of sales figures at RandomNumbers-R-Us, the nation’s leading vendor of voting machines. She believes it will be wonderful and joyous (and, of course, fun) to use =.042 and =.846. Which of the following statements best describes the results of her double exponential smoothing? _____ Her results will be incorrect, because her  and her  don’t add to 1._____ Because the sample size is so large, her smoothed values will be very close to the actual data._____ Location estimates will react very rapidly to shifts in the data, while estimates of the trend will tend to be similar from one data point to the next._____ Trend estimates will react very rapidly to shifts in the data, while estimates of the location will tend to be similar from one data point to the next.Question 6 [2 points]:The court system in the Kingdom of Boravia believes that the defendant in a criminal case should be “presumed innocent until proven guilty beyond a reasonable doubt.” Boravia is unique, however, in having a strict quantitative definition of what constitutes “reasonable” doubt.At present, juries in Boravia are required by law to use statistical methods in assessing the defendant’s guilt, and to reject the null hypothesis of innocence if (and only if) the p-value from their test is less than =.01. The Attorney General of Boravia has proposed a constitutional amendment that would change this value to =.05. (“It’s more traditional,” explained the AG in a recent interview.) If the amendment were ratified, what effect would this have on the Boravian court system?_____ More innocent people would be convicted, while more guilty people would be set free._____ More guilty people would be convicted, while more innocent people would be set free._____ More guilty people would be convicted, but more innocent people would be convicted._____ More innocent people would be set free, but more guilty people would be set free.Question 7 [2 points]:Balph Snerdwell randomly selects five students from this class, and collects data on the number of hours of sleep they got last night. From these data, he computes a 95% confidence interval as 6.42 + 2. What may he conclude from this interval?_____ He’s 95% confident that the five people in his sample averaged less than 8 hours of sleep last night._____ Out of the entire class, 95% of the students got between 4.42 and 8.42 hours of sleep last night._____ A hypothesis test of H0:  = 8 would not be rejected._____ The population mean is between 4.42 and 8.42 hours._____ None of the above.Question 8 [4 points]:Continuing the example from above: What did Balph obtain as the sample mean and the sample standard deviation for his five data points? (If we can’t find these numbers from the information given, explain why.)Question 9 [3 points]:Recall that the security market line is the regression line relating the expected return of a stock (Y) to its risk (X). The intercept of that line may be interpreted as “the return you expect when you incur 0 risk.” Since short-term U.S. Treasury bills are a good proxy for this risk-free rate, we know that the intercept of the security market line should equal the Treasury bill rate. What statistical procedure would we