STAT 200: Introduction to StatisticsFinal Examination, Fall 2015 OL4/US2Page 1 of 6STAT 200OL4/US2 SectionsFinal ExamFall 2015The final exam will be posted at 12:01 am on December 11, andit is due at 11:59 pm on December 13, 2015. Eastern Time isour reference time.This is an open-book exam. You may refer to your text and other coursematerials as you work on the exam, and you may use a calculator. You mustcomplete the exam individually. Neither collaboration nor consultation withothers is allowed.Answer all 25 questions. Make sure your answers are as complete as possible.Show all of your work and reasoning. In particular, when there arecalculations involved, you must show how you come up with your answerswith critical work and/or necessary tables. Answers that come straight fromprograms or software packages will not be accepted. If you need to usesoftware (for example, Excel) and /or online or hand-held calculators to aid inyour calculation, please cite the sources and explain how you get the results.Record your answers and work on the separate answer sheet provided.This exam has 200 total points.You must include the Honor Pledge on the title page of your submitted finalexam. Exams submitted without the Honor Pledge will not be accepted.STAT 200: Introduction to Statistics1.Final Examination, Fall 2015 OL4/US2True or False. Justify for full credit.Page 2 of 6(15 pts)(a) If the variance of a data set is zero, then all the observations in this data set are zero.(b) If P(A) = 0.4 , P(B) = 0.5, and A and B are disjoint, then P(A AND B) = 0.9.(c) Assume X follows a continuous distribution which is symmetric about 0. If, then.(d) A 95% confidence interval is wider than a 90% confidence interval of the sameparameter.(e) In a right-tailed test, the value of the test statistic is 1.5. If we know the test statisticfollows a Studentâs t-distribution with P(T < 1.5) = 0.96, then we fail to reject thenull hypothesis at 0.05 level of significance .Refer to the following frequency distribution for Questions 2, 3, 4, and 5. Show all work. Just theanswer, without supporting work, will receive no credit.The frequency distribution below shows the distribution for checkout time (in minutes) inUMUC MiniMart between 3:00 and 4:00 PM on a Friday afternoon.Checkout Time (in minutes) Frequency Relative Frequency1.0 – 1.932.0 – 2.9120.203.0 – 3.94.0 – 4.935.0 -5.9Total252.Complete the frequency table with frequency and relative frequency. Express the relativefrequency to two decimal places.(5 pts)3.What percentage of the checkout times was at least 3 minutes?(3 pts)4.In what class interval must the median lie? Explain your answer.(5 pts)5.Does this distribution have positive skew or negative skew? Why?(2 pts)Refer to the following information for Questions 6 and 7. Show all work. Just the answer,without supporting work, will receive no credit.Consider selecting one card at a time from a 52-card deck. (Note: There are 4 aces in a deck ofcards)6.If the card selection is without replacement, what is the probability that the first card is an ace andthe second card is also an ace? (Express the answer in simplest fraction form)(5 pts)STAT 200: Introduction to StatisticsFinal Examination, Fall 2015 OL4/US2Page 3 of 67.If the card selection is with replacement, what is the probability that the first card is an ace andthe second card is also an ace? (Express the answer in simplest fraction form)(5 pts)Refer to the following situation for Questions 8, 9, and 10.The five-number summary below shows the grade distribution of two STAT 200 quizzes fora sample of 500 students.Quiz 1Quiz 2MinimumQ1MedianQ3Maximum1520303555508590100100For each question, give your answer as one of the following: (a) Quiz 1; (b) Quiz 2; (c) Both quizzeshave the same value requested; (d) It is impossible to tell using only the given information. Thenexplain your answer in each case.(4 pts each)8.9.10.Which quiz has less interquartile range in grade distribution?Which quiz has the greater percentage of students with grades 80 or over?Which quiz has a greater percentage of students with grades less than or equal to 50?Refer to the following information for Questions 11, 12, and 13. Show all work. Just the answer,without supporting work, will receive no credit.There are 1000 students in a high school. Among the 1000 students, 800 students have alaptop, and 300 students have a tablet. 250 students have both devices.11.12.13.14.What is the probability that a randomly selected student has neither device?(10 pts)What is the probability that a randomly selected student has a tablet, given that he/she hasa laptop?(5 pts)Let event A be the selected student having a laptop, and event B be the selected studenthaving a tablet. Are A and B independent events? Why or why not?(5 pts)A combination lock uses three distinctive numbers between 0 and 39 inclusive. How manydifferent ways can a sequence of three numbers be selected? (Show work)(5 pts)15.Let random variable x represent the number of heads when a fair coin is tossed threetimes. Show all work. Just the answer, without supporting work, will receive no credit.(a)(b)Construct a table describing the probability distribution.(5 pts)Determine the mean and standard deviation of x. (Round the answer to two decimal places)(10 pts)STAT 200: Introduction to StatisticsFinal Examination, Fall 2015 OL4/US2Page 4 of 616.Mimi just started her tennis class three weeks ago. On average, she is able to return 25% of heropponentâs serves. Assume her opponent serves 10 times.(a)(b)Let X be the number of returns that Mimi gets. As we know, the distribution of X is a binomialprobability distribution. What is the number of trials (n), probability of successes (p) andprobability of failures (q), respectively?(5 pts)Find the probability that that she returns at least 1 of the 10 serves from her opponent.(Show work) (10 pts)Refer to the following information for Questions 17, 18, and 19. Show all work. Just the answer,without supporting work, will receive no credit.The lengths of mature jalapeño fruits are normally distributed with a mean of 3 inches and astandard deviation of 1 inch.17.18.19.What is the probability that a randomly selected mature jalapeño fruit is between 1.5 and 3.5inches long?(5 pts)Find the 90th percentile of the jalapeño fruit length distribution.(5 pts)If a random sample of 400 mature jalapeño fruits is selected, what is the standard deviation of thesample mean?(5 pts)20.A random sample of 100 light bulbs has a mean lifetime of 3000 hours. Assume that thepopulation standard deviation of the lifetime is 500 hours. Construct a 90% confidence intervalestimate of the mean lifetime. Show all work. Just the answer, without supporting work, willreceive no credit.(8 pts)21.Consider the hypothesis test given byH 0 : p 0.5H1 : p 0.5In a random sample of 400 subjects, the sample proportion is found to be pË 0.55 .(a) Determine the test statistic. Show all work; writing the correct test statistic, withoutsupporting work, will receive no credit.(b) Determine the P-value for this test. Show all work; writing the correct P-value,without supporting work, will receive no credit.(c) Is there sufficient evidence to justify the rejection of H 0 at the 0.01 level?Explain.(15 pts)STAT 200: Introduction to Statistics22.Final Examination, Fall 2015 OL4/US2Page 5 of 6Consumption of large amounts of alcohol is known to increase reaction time. Toinvestigate the effects of small amounts of alcohol, reaction time was recorded for fiveindividuals before and after the consumption of 2 ounces of alcohol. Do the data belowsuggest that consumption of 2 ounces of alcohol increases mean reaction time?Subject12345Reaction Time (seconds)BeforeAfter6788467998Assume we want to use a 0.05 significance level to test the claim.(a) Identify the null hypothesis and the alternative hypothesis.(b) Determine the test statistic. Show all work; writing the correct test statistic, withoutsupporting work, will receive no credit.(c) Determine the P-value. Show all work; writing the correct P-value, withoutsupporting work, will receive no credit.(d) Is there sufficient evidence to support the claim that consumption of 2 ounces ofalcohol increases mean reaction time? Justify your conclusion.(15 pts)23.The UMUC MiniMart sells five different types of coffee mugs. The manager reports thatthe five types are equally popular. Suppose that a sample of 500 purchases yieldsobserved counts 110, 100, 110, 100, and 80 for types 1, 2, 3, 4, and 5, respectively.TypeNumber of Mugs1110210031104100580Assume we want to use a 0.05 significance level to test the claim that the five types areequally popular.(a) Identify the null hypothesis and the alternative hypothesis.(b) Determine the test statistic. Show all work; writing the correct test statistic, withoutsupporting work, will receive no credit.(c) Determine the P-value for the test. Show all work; writing the correct P-value,without supporting work, will receive no credit.(d) Is there sufficient evidence to support the managerâs claim that the four types areequally popular? Justify your answer.(15 pts)STAT 200: Introduction to StatisticsFinal Examination, Fall 2015 OL4/US2Page 6 of 624.A random sample of 4 professional athletes produced the following data where x is thenumber of endorsements the player has and y is the amount of money made (in millions ofdollars).xy(a)(b)01123558Find an equation of the least squares regression line. Show all work; writing the correctequation, without supporting work, will receive no credit.(10 pts)Based on the equation from part (a), what is the predicted value of y if x = 2? Show allwork and justify your answer.(5 pts)25. A STAT 200 instructor is interested in whether there is any variation in the final exam gradesbetween her two classes Data collected from the two classes are as follows:Her null hypothesis and alternative hypothesis are:(a)(b)(c)Determine the test statistic. Show all work; writing the correct test statistic, withoutsupporting work, will receive no credit.Determine the P-value for this test. Show all work; writing the correct P-value, withoutsupporting work, will receive no credit.Is there sufficient evidence to justify the rejection of H 0 at the significance level of 0.05?Explain.(10 pts)
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