DS350 – QUANTITATIVE METHODS FOR BUSINESS DECISIONSSPRING SEMESTER 2004“Knowledge Festival” in Celebration of the Friday 13th HolidayThis exam is given under the provisions of the Honor System; the word “Pledged” before yoursignature indicates your ongoing ongoing adherence to the provisions of that System.Answer the following questions in the space provided. SHOW YOUR WORK when applicable.Unless the problem indicates otherwise, use the traditional confidence level of 95% and thetraditional significance level of =.05. Relative problem weights are given in brackets; thesetotal 100 points. Enjoy!!Question 1 [4 points]:Alphonso Ferrabosco II is conducting a hypothesis test. He computes a p-value of .0042. What conclusion should he draw?_____ Reject the null. There is enough evidence to believe the null is false._____ Reject the null. There is not enough evidence to believe the null is true._____ Don’t reject the null. There is enough evidence to believe the null is true._____ Don’t reject the null. There is not enough evidence to believe the null is false.Question 2 [4 points]:Balph Snerdwell has computed a 95% confidence interval from a data set. Berengaria Naverre has computed an 85% confidence interval, using the same data. Which of the following is true?_____ Balph’s confidence interval will be wider than Berengaria’s_____ Balph’s and Berengaria’s confidence intervals will be the same size._____ Berengaria’s confidence interval will be wider than Balph’s._____ We cannot tell from the information given.Question 3 [4 points]:Clorinda Cragdingle decides to be somewhat nontraditional, and conducts a hypothesis test using a significance level of =.42, rather than =.05. What does this imply about her results?_____ She will make more Type I errors but fewer Type II errors._____ She will make more Type II errors but fewer Type I errors._____ She will make fewer Type I errors and fewer Type II errors._____ She will make more Type I errors and more Type II errors.Question 4 [4 points]:Recall that the Literary Digest was badly mistaken in its election poll in the 1936 presidential race. What were the primary reason(s) for this error? (NOTE: there may be more than one correct answer; check all that apply.)_____ Their sample size was too small._____ They had never conducted a poll before._____ Their sample was not representative of the population._____ Many people did not respond to the survey._____ Many people lied when they answered the survey.Question 5 [4 points]:Compute a sample standard deviation for the following numbers. Show your work.8 9 5 2Question 6 [12 points, divided as indicated]:Dietrich Buxtehude believes that sleeping with a statistics book under the pillow will improve a student’s grade on the “knowledge festival.” He recruits twelve of his friends to participate in a study. Half of them (randomly assigned) sleep with the book under the pillow; the other half do not. He compares their average “big quiz” grades.a) [2] This is a {pick one} controlled experiment observational studyb) [6] State Dietrich’s null and alternative hypotheses, in words and in symbols.c) [4] What would a Type I error be, in this situation?Question 7 [4 points]:Suppose that, in the previous problem, Dietrich had computed a p-value of .42. Which one of the following is the best interpretation of that p-value?_____ Students score 42% higher with a book under their pillow._____ There’s a 42% chance that sleeping with a book under the pillow works._____ There’s a 42% chance that sleeping with a book under the pillow doesn’t work._____ Even if putting the book under the pillow doesn’t help, there’s still a 42% chance of getting a result similar to Dietrich’s experiment.Question 8 [4 points]:Continuing with the same scenario as Questions 6 and 7, above: Dietrich has gotten a p-value of .42. Is this result statistically significant? Explain.Question 9 [4 points]:Which of the following statements is/are true, regarding face-to-face vs. mail surveys? (NOTE: There may be more than one correct answer; check all that apply.)_____ Face-to-face surveys tend to have higher response rates._____ You get more reliable data on sensitive questions from face-to-face surveys._____ Costs tend to be lower in mail surveys._____ Face-to-face surveys generally allow a wider range of types of questions.Question 10 [12 points, divided as indicated]:Euterpe Waldfogel wishes to estimate the average starting salary for the hunderds of basketweaving majors graduating from the Rollens College of Decorative Arts. She surveys a random sample of ten recent graduates, and notes that their average starting salary was $18,400, with a standard deviation of $2400.a) [8] Give a confidence interval for the average starting salary for all Rollens College basketweaving majors.b) [4] Suppose Euterpe were to find out that Rollens College had only graduated ten basketweaving majors in its entire history. How would this change the answer in Part A? Explain.Question 11 [4 points]:Euterpe also computed a confidence interval for the mean starting salary for flycasting majors at Rollens College. Her interval was $20,000 + $2000. Which of the following is the best interpretation of that interval?_____ Most (95%) of the Rollens flycasting grads have starting salaries between $18,000 and $22,000._____ If she were to survey all Rollens flycasting grads, and average their starting salaries, she’dprobably (95% chance) get an answer between $18,000 and $22,000._____ She’s pretty sure (95% confidence) that the average starting salary for the Rollens flycasting grads in her sample was between $18,000 and $22,000._____ She’s 95% correct in believing that Rollens flycasting grads have starting salaries between$18,000 and $22,000. Question 12 [4 points]:Suppose, in Question 11, Euterpe were testing H0: =21,000, versus a two-tailed alternative. Should she reject the null hypothesis?_____ Yes _____ No _____ We can’t tell from the information given.Explain.Question 13 [26 points, divided as indicated]:Gracetta Squornshellous notes that the Dow Jones Industrial Average has increased on 51.42% of the days since its inception. Gracetta suspects that Friday the Thirteenth is an unluckyday in the stock market. She investigates her claim by checking whether the Dow went up or down, on each of the last forty Friday-the-Thirteenths.a) [6] State Gracetta’s null and