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Stat 200 Final Exam

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Stat 200 Final Exam;1. Determine whether the given value is a statistic or parameter. (4 pts);(a) In a STAT 200 student survey, 20% of the respondents said that they had to take time off from work to study for the course.;(b) The average lifetime of all street lights in UMUC Academic Center is 20,000 hours.;2. True of False. (8 pts);(a) Mean is a better measure of center than median because mean is not affected by extreme values from a data set.;(b) If the variance from a data set is zero, then all the observations in this data set are the same.;(c) It is possible that a data set does not have a mode.;(d) P(AandA) 1, whereAis the complement ofA.;Refer to the following frequency distribution for Questions 3, 4, 5, and 6. Show all work. Just the answer, without supporting work, will receive no credit.;The frequency distribution below shows the distribution for checkout time (in minutes) in UMUC MiniMart between 3:00 and 4:00 PM on a Friday afternoon.;Checkout Time (in minutes);Frequency;1.0 - 1.9;6;2.0 - 2.9;5;3.0 - 3.9;4;4.0 - 4.9;3;5.0 - 5.9;2;STAT200: Introduction to Statistics Final Examination, Fall 2014 OL1 Page 3 of 6;3.;What percentage of the checkout times was at least 4 minutes?;(5 pts);4.;Calculate the mean of this frequency distribution.;(5 pts);5. Calculate the standard deviation of this frequency distribution. (Round the answer to two;decimal places) (10 pts);6. Assume that the smallest observation in this dataset is 1.2 minutes. Suppose this observation were incorrectly recorded as 0.12 instead of 1.2. Will the mean increase;decrease, or remain the same? Will the median increase, decrease or remain the same? Explain your answers. (5 pts);Refer to the following data to answer questions 7 and 8. Show all work. Just the answer, without supporting work, will receive no credit.;A random sample of STAT200 weekly study times in hours is as follows;1 13 15 18 20;7. Find the standard deviation. (Round the answer to two decimal places) (10 pts);8. Are any of these study times considered unusual based on the Range Rule of Thumb?;Show work and explain. (5 pts);Refer to the following information for Questions 9, 10 and 11. Show all work. Just the answer, without supporting work, will receive no credit.;Consider selecting one card at a time without replacement from a 52-card deck. Let event A be the first card is a heart, and event B be the second card is a heart.;9. What is the probability that the first card is a heart and the second card is also a heart?;(Express the answer in simplest fraction form) (8 pts);10. What is the probability that the second card is a heart, given that the first card is a heart?;(Express the answer in simplest fraction form);(8 pts);11.;Are A and B independent? Why or why not?;(2 pts);Refer to the following information for Questions 12 and 13. Show all work. Just the answer, without supporting work, will receive no credit.;There are 1500 juniors in a college. Among the 1500 juniors, 200 students are taking STAT200, and 100 students are taking PSYC300. There are 50 students taking both courses.;12. What is the probability that a randomly selected junior is in neither of the two courses?;(10 pts) 13. What is the probability that a randomly selected junior takes only one course? (10 pts);Refer to the following information for Questions 14, and 15. Show all work. Just the answer, without supporting work, will receive no credit.;STAT200: Introduction to Statistics Final Examination, Fall 2014 OL1 Page 4 of 6;UMUC STAT Club must appoint a president, a vice president, and a treasurer. It must also select three members for the STAT Olympics team. There are 10 qualified candidates, and officers can also be on the STAT Olympics team.;14.;How many different ways can the officers be appointed?;(10 pts);15.;How many different ways can the STAT Olympics team be selected?;(10 pts);Questions 16 and 17 involve the random variable x with probability distribution given below.;Show all work. Just the answer, without supporting work, will receive no credit.;x;-1;0;1;2;5;P(x);0.1;0.1;0.4;0.1;0.3;16.;Determine the expected value of x.;(5 pts);17.;Determine the standard deviation of x.(Round the answer to two decimal places);(10 pts);Consider the following situation for Questions 18, 19 and 20. Show all work. Just the answer, without supporting work, will receive no credit.;Mimi made random guesses at 5 true-or-false questions in a STAT 200 pop quiz. Let random number X be the number of correct answers Mimi got. As we know, the distribution of X is a binomial probability distribution. Please answer the following questions;18. What is the number of trials (n), probability of successes (p) and probability of failures (q);respectively?;(5 pts);19.;Find the probability that she got at least 3 correct answers.;(10 pts);20. Find the mean and standard deviation for the probability distribution. (Round the answer to two;decimal places) (10 pts);Refer to the following information for Questions 21, 22, and 23. Show all work. Just the answer, without supporting work, will receive no credit.;The heights of dogwood trees are normally distributed with a mean of 9 feet and a standard deviation of 3 feet.;21. What is the probability that a randomly selected dogwood tree is between 6 and 15 feet tall?;(10 pts);22.;Find the 80th percentile of the dogwood tree height distribution.;(5 pts);23. If a random sample of 144 dogwood trees is selected, what is the standard deviation of the sample;mean? (5 pts);24. A random sample of 100 GMAT scores has a mean of 500. Assume that GMAT scoreshave a population standard deviation of 120. Construct a 95% confidence interval estimate of the;STAT200: Introduction to Statistics Final Examination, Fall 2014 OL1 Page 5 of 6;mean GMAT scores. Show all work. Just the answer, without supporting work, will receive no credit.;(15 pts);25. Given a sample size of 100, with sample mean 730 and sample standard deviation 100;we perform the following hypothesis test at the;0.05 level.;H0: 750;H1: 750;(a) Determine the test statistic. Show all work, writing the correct test statistic, without supporting work, will receive no credit.;(b) Determine the critical value. Show all work, writing the correct critical value;without supporting work, will receive no credit.;(c) What is your conclusion of the test? Please explain. (20 pts);26. Consider the hypothesis test given by;H 0: p 0.5 H1: p0.5;In a random sample of 225 subjects, the sample proportion is found to be p? 0.55.;(a) Determine the test statistic. Show all work, writing the correct test statistic, without supporting 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 H0 at the0.01 level?;Explain. (20 pts);27. 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 24 hours later. The result is shown in the following table.;Number of Words Recalled;Subject;1 hour later;24 hours later;1;14;10;2;18;14;3;11;9;4;16;12;5;15;12;STAT200: Introduction to Statistics Final Examination, Fall 2014 OL1 Page 6 of 6;Is there evidence to suggest that the mean number of words recalled after 1 hour exceeds the mean recall after 24 hours by more than 3?;Assume we want to use a 0.01 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 supporting work, will receive no credit.;(c) Determine the critical value. Show all work, writing the correct critical 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 1 hour exceeds the mean recall after 24 hours by more than 3? Justify your conclusion. (25 pts);Refer to the following data for Questions 28 and 29.;x;0;-1;3;2;5;y;3;-2;3;6;8;28. Find an equation of the least squares regression line. Show all work, writing the correct;equation, without supporting work, will receive no credit. (15 pts);29. Based on the equation from # 28, what is the predicted value of y if x = 4? Show all work;and justify your answer. (10 pts);30.;The UMUC Bookstore sells three different types of coffee mugs. The manager reported;that the three types are purchased in proportions: 50%, 30%, and 20%, respectively.;Suppose that a sample of 100 purchases yields observed counts 46, 28, and 26 for types;1, 2, and 3, respectively.;Type;1;2;3;Number;46;28;26;Assume we want to use a 0.10 significance level to test the claim that the reported;proportions are correct.;(a);Identify the null hypothesis and the alternative hypothesis.;(b);Determine the test statistic. Show all work, writing the correct test statistic, without;supporting work, will receive no credit.;(c);Determine the critical value. Show all work, writing the correct critical value;without supporting work, will receive no credit.;(d);Is there sufficient evidence to support the claim that the reported proportions are;correct? Justify your answer.

 

Paper#31540 | Written in 18-Jul-2015

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