Question Number: 375

STAT 200OL4/US2 SectionsFinal ExamFall 2017The final exam will be posted at 12:01 am on December 15, and itis due at 11:59 pm on December 17, 2017. Eastern Time is ourreference time.This is an open-book exam. You may refer to your text and other course materialsfor the current course as you work on the exam, and you may use a calculator.You must complete the exam individually. Neither collaboration nor consultationwith others is allowed. It is a violation of the UMUC Academic Dishonesty andPlagiarism policy to use unauthorized materials or work from others.Answer all 20 questions. Make sure your answers are as complete as possible.Show all of your supporting work and reasoning. Answers that come straightfrom calculators, programs or software packages without any explanation will notbe accepted. If you need to use technology (for example, Excel, online or handheld calculators, statistical packages) to aid in your calculation, you must cite thesources and explain how you get the results.Record your answers and work on the separate answer sheet provided.This exam has 20 questions; 5% for each question.You must include the Honor Pledge on the title page of your submitted final exam.Exams submitted without the Honor Pledge will not be accepted.STAT 200: Introduction to Statistics Final Examination, Fall 2017 OL4 Page 2 of 91. True or False. Justify for full credit.(a) If A and B are disjoint, P(A) = 0.4 and P(B) = 0.5, then P(A OR B) = 0.9.(b) If the variance for a data set is zero, then all the observations in this data set must beidentical.(c) There may be more than one mode in a data set.(d) A 90% confidence interval is wider than a 95% confidence interval of the same parameter.(e) In a right-tailed test, the value of the test statistic is 2. The test statistic follows adistribution with the distribution curve shown below. If we know the shaded area is 0.03,then we have sufficient evidence to reject the null hypothesis at 0.05 level of significance.2. Choose the best answer. Justify for full credit.(a) UMUC STAT Club wanted to estimate the study hours of STAT 200 students. One STAT 200section was randomly selected and all students from that section were asked to fill out thequestionnaire. This type of sampling is called:(i) cluster(ii) convenience(iii) systematic(iv) stratified(b) A study was conducted at a local college to analyze the trend of average GPA of all studentsgraduated from the college. According to the Registrar, the average GPA for students witheconomics major from the class of 2016 is 3.5. The value 3.5 is a(i) statistic(ii) parameter(iii) cannot be determinedSTAT 200: Introduction to Statistics Final Examination, Fall 2017 OL4 Page 3 of 9(c) The hotel ratings are usually on a scale from 0 star to 5 stars. The level of this measurement is(i) interval(ii) nominal(iii) ordinal(iv) ratio(d) 500 students took a chemistry test. You sampled 100 students to estimate the average score andthe standard deviation. How many degrees of freedom were there in the estimation of thestandard deviation?(i) 99(ii) 100(iii) 499(iv) 500(e) You choose an alpha level of 0.01 and then analyze your data. What is the probability that youwill make a Type I error given that the null hypothesis is true?(i) 0.025(ii) 0.05(iii) 0.01(iv) 0.103. A random sample of 500 students was chosen from UMUC STAT 200 classes. The frequencydistribution below shows the distribution for study time each week (in hours). (Show all work.Just the answer, without supporting work, will receive no credit.)Study Time (in hours) Frequency Relative Frequency0.0 – 5.0 405.1 – 10.0 10010.1 – 15.0 0.2515.1 - 20.0 12020.1 – 25.0Total 500(a) Complete the frequency table with frequency and relative frequency. Express the relativefrequency to two decimal places.(b) What percentage of the study times was not more than 15 hours?(c) In what class interval must the median lie? 5.1 – 10.0, 10.1 -15.0, 15.1 – 20.0, or 20.1 – 25.0?Why?STAT 200: Introduction to Statistics Final Examination, Fall 2017 OL4 Page 4 of 94. The five-number summary below shows the grade distribution of a STAT 200 quiz for asample of 500 students.Answer each question based on the given information, and explain your answer in each case.(a) What is the minimum in the grade distribution?(b) Which quarter has the smallest spread of data? What is that spread?(c) Find the interquartile range in the grade distribution.(d) Are there more students in the score band of 45- 65 or 65 - 85? Why?(e) Can the average score be determined based on the given information? Why or why not?5. A basket contains 1 white balls, 5 yellow balls, and 4 red balls. Consider selecting one ball at atime from the basket. (Show all work. Just the answer, without supporting work, will receiveno credit.)(a) Assuming the ball selection is without replacement. What is the probability that the first ball iswhite and the second ball is red?(b) Assuming the ball selection is with replacement. What is the probability that the first ball is redand the second ball is also red?6. There are 1000 juniors in a college. Among the 1000 juniors, 400 students are takingSTAT200, and 700 students are taking PSYC300. There are 200 students taking both courses.Let S be the event that a randomly selected student takes STAT200, and P be the event that arandomly selected student takes PSYC300. (Show all work. Just the answer, withoutsupporting work, will receive no credit.)(a) Provide a written description of the complement event of (S OR P).(b) What is the probability of complement event of (S OR P)?STAT 200: Introduction to Statistics Final Examination, Fall 2017 OL4 Page 5 of 97. Consider rolling a fair 6-faced die twice. Let A be the event that the sum of the two rolls isequal to 7, and B be the event that the first one is an odd number.(a) What is the probability that the sum of the two rolls is equal to 7 given that the first one is anodd number? Show all work. Just the answer, without supporting work, will receive no credit.(b) Are event A and event B independent? Explain.8. Answer the following two questions. (Show all work. Just the answer, without supportingwork, will receive no credit).(a) UMUC Stat Club is sending a delegate of 2 members to attend the 2018 Joint StatisticalMeeting in Vancouver. There are 10 qualified candidates. How many different ways can thedelegate be selected?(b) A bike courier needs to make deliveries at 5 different locations. How many different routes canhe take?9. Imagine you are in a game show. There are 20 prizes hidden on a game board with 100 spaces.One prize is worth $50, nine are worth $20, and another ten are worth $10. You have to pay $5to the host if your choice is not correct. Let the random variable x be the money you get orlose. Show all work. Just the answer, without supporting work, will receive no credit.(a) Complete the following probability distribution.x P(x)-$5$10$20$50(b) What is your expected winning or loss in this game? Be specific in your answer whether it’swinning or loss.10. Mimi joined UMUC basketball team in spring 2017. On average, she is able to score 20% of the fieldgoals. Assume she tries 10 field goals in a game.(a) Let X be the number of field goals that Mimi scores in the game. As we know, the distribution of X isa binomial probability distribution. What is the number of trials (n), probability of successes (p) andprobability of failures (q), respectively?(b) Find the probability that Mimi scores at least 3 of the 10 field goals. (round the answer to 3 decimalplaces) Show all work. Just the answer, without supporting work, will receive no credit.STAT 200: Introduction to Statistics Final Examination, Fall 2017 OL4 Page 6 of 911. A research concludes that the number of hours of exercise per week for adults is normallydistributed with a mean of 4 hours and a standard deviation of 2.5 hours. Show all work. Just theanswer, without supporting work, will receive no credit.(a) What is the probability that a randomly selected adult has at least 5 hours of exercise per week (roundthe answer to 4 decimal places)(b) Find the 75th percentile for the distribution of exercise time per week. (round the answer to 2 decimalplaces)12. Assume the SAT Mathematics Level 2 test scores are normally distributed with a mean of 500and a standard deviation of 100. Show all work. Just the answer, without supporting work, willreceive no credit.(a) Consider all random samples of 64 test scores. What is the standard deviation of the samplemeans? (Round your answer to three decimal places)(b) What is the probability that 64 randomly selected test scores will have a mean test score that isbetween 490 and 520? (Round your answer to four decimal places)13. In a study designed to test the effectiveness of garlic for lowering cholesterol, 49 adults weretreated with garlic tablets. Cholesterol levels were measured before and after the treatment. Thechanges in their LDL cholesterol (in mg/dL) have a mean of 3 and standard deviation of 10.Construct a 95% confidence interval estimate of the mean change in LDL cholesterol after thegarlic tablet treatment. Show all work. Just the answer, without supporting work, will receiveno credit.14. Mimi conducted a survey on a random sample of 100 adults. 75 adults in the sample chosebanana as his / her favorite fruit. Construct a 90% confidence interval estimate of the proportionof adults whose favorite fruit is banana. Show all work. Just the answer, without supportingwork, will receive no credit.15. A researcher is interested in testing the claim that more than 80% of the adults believe inglobal warming. She conducted a survey on a random sample of 800 adults. The surveyshowed that 650 adults in the sample believe in global warming.Assume the researcher wants 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, without supportingwork, will receive no credit.(c) Determine the P-value for this test. Show all work; writing the correct P-value, withoutsupporting work, will receive no credit.(d) Is there sufficient evidence to support the claim that more than 80% of adults believe in globalwarming? Explain.STAT 200: Introduction to Statistics Final Examination, Fall 2017 OL4 Page 7 of 916. In a study of memory recall, 5 people were given 10 minutes to memorize a list of 20 words.Each was asked to list as many of the words as he or she could remember both 1 hour and 24hours later. The result is shown in the following table.Number of Words RecalledSubject 1 hour later 24 hours later1 13 132 18 143 12 114 15 145 11 11Is there evidence to suggest that the mean number of words recalled after 1 hour exceeds themean recall after 24 hours? Assume we want to use a 0.05 significance level to test theclaim.(a) Identify the null hypothesis and the alternative hypothesis.(b) Determine the test statistic. Show all work; writing the correct test statistic, without supportingwork, will receive no credit.(c) Determine the P-value. Show all work; writing the correct P-value, without supporting work,will receive no credit.(d) Is there sufficient evidence to support the claim that the mean number of words recalled after 1hour exceeds the mean recall after 24 hours? Justify your conclusion.17. John oversees a bottle-filling machine in a company. The amount of fluid dispensed into eachbottle is approximately normally distributed with an unknown population standard deviation.On a particular day, a random sample of 400 bottles yielded a mean of 357.2 ml and a standarddeviation of 16.2 ml. John then concluded that the population standard deviation of the fluiddispense amount by the machine is greater than 15 ml.The lead engineer wants to use a 0.05 significance level to test John’s claim.(a) Identify the null hypothesis and 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 this test. Show all work; writing the correct P-value, withoutsupporting work, will receive no credit.(d) Is there sufficient evidence to support John’s claim that the population standard deviation of thefluid dispense amount by the machine is greater than 15 ml? Explain.STAT 200: Introduction to Statistics Final Examination, Fall 2017 OL4 Page 8 of 918. The UMUC Daily News reported that the color distribution for plain M&M’s was: 35%brown, 30% yellow, 15% orange, 10% green, and 10% tan. Each piece of candy in a randomsample of 200 plain M&M’s was classified according to color, and the results are listed below.Use a 0.05 significance level to test the claim that the published color distribution is correct.Show all work and justify your answer.Color Brown Yellow Orange Green TanNumber 80 45 30 30 15(a) Identify the null hypothesis and the alternative hypothesis.(b) Determine the test statistic. Show all work; writing the correct test statistic, without supportingwork, will receive no credit.(c) Determine the P-value. Show all work; writing the correct P- value, without supporting work,will receive no credit.(d) Is there sufficient evidence to support the claim that the published color distribution is correct?Justify your answer.19. A STAT 200 instructor believes that the average quiz score is a good predictor of final examscore. A random sample of 10 students produced the following data where x is the average quizscore and y is the final exam score.x 72 96 55 65 100 50 85 70 74 85y 72 98 50 70 96 60 83 75 77 87(a) Find an equation of the least squares regression line. Show all work; writing the correctequation, without supporting work, will receive no credit.(b) Based on the equation from part (a), what is the predicted final exam score if the average quizscore is 80? Show all work and justify your answer.