STAT 200 OL4 / OL2 Sections Final Exam Fall 2014
1. True or False. Justify for full credit score. (25 pts) (a) If there isn't a linear correlation between two variables, then these two variables usually are not associated in any manner. STAT200 : Introduction to Statistics Last Examination, Fall 2014 OL4 / US2 Web page 2 of 6 (b) If the variance from an information set is zero, then all of the observations on this information set are an identical. (c) P( A and A)=1, the place Ais the complement of A. (d) In a speculation testing, if the P-value is lower than the importance stage ?, we reject the null speculation. (e) The quantity of milk in a jug of milk is 128 oz. The worth 128 is from a discrete information set. .gif">.gif">.gif">.gif">.gif">.gif"> Confer with the next frequency distribution for Questions 2, three, four, and 5. Present all work. Simply the reply, with out supporting work, will obtain no credit score. The frequency distribution beneath exhibits the distribution for checkout time (in minutes) in UMUC MiniMart between three:00 and four:00 PM on a Friday afternoon. Checkout Time (in minutes) Frequency 1.zero - 1.9 2 2.zero - 2.9 12 three.zero - three.9 2 four.zero - four.9 four 2. What share of the checkout instances was lower than three minutes? (5 pts) three. In what class interval should the median lie? Clarify your reply. (5 pts) four. Calculate the imply of this frequency distribution. (5 pts) 5. Calculate the usual deviation of this frequency distribution. (Spherical the reply to 2 decimal locations) (10 pts) .gif">.gif">.gif">.gif"> Confer with the next information to reply questions 6, 7 and eight. Present all work. Simply the reply, with out supporting work, will obtain no credit score. A random pattern of STAT200 weekly research instances in hours is as follows: 2 15 15 18 40 6. Discover the pattern customary deviation. (Around the reply to 2 decimal locations) (10 pts) 7. Discover the coefficient of variation. (5 pts) eight. Are any of those research instances thought of uncommon primarily based on the Vary Rule of Thumb? Present work and clarify. (5 pts) .gif">.gif">.gif">.gif">.gif"> Confer with the next data for Questions 9, 10 and 11. Present all work. Simply the reply, with out supporting work, will obtain no credit score. Contemplate deciding on one card at a time from a 52-card deck. Let occasion A be the primary card is an ace, and occasion B be the second card is an ace. (Word: There are four aces in a deck of playing cards) STAT200 : Introduction to Statistics Last Examination, Fall 2014 OL4 / US2 Web page three of 6 9. If the cardboard choice is with out substitute, what's the chance that the first card is an ace and the second card can also be an ace? (Specific the reply in easiest fraction kind) (10 pts) 10. If the cardboard choice is with substitute, what's the chance that the primary card is an ace and the second card can also be an ace? (Specific the reply in easiest fraction kind) (10 pts) 11. Are A and B unbiased when the choice is with substitute? Why or why not? (5 pts) .gif">.gif">.gif">.gif"> Confer with the next data for Questions 12 and 13. Present all work. Simply the reply, with out supporting work, will obtain no credit score. There are 1000 juniors in a school. Among the many 1000 juniors, 200 college students are taking STAT200, and 100 college students are taking PSYC300. There are 50 college students taking each programs. 12. What is the chance that a randomly chosen junior is taking not less than one in every of these two programs? (10 pts) 13. What is the chance that a randomly chosen junior is taking PSYC300, given that he/she is taking STAT200? (10 pts) .gif">.gif">.gif">.gif"> 14. UMUC Stat Membership should appoint a president, a vp, and a treasurer. There are 10 certified candidates. What number of other ways can the officers be appointed? (5 pts) .gif">.gif">.gif">.gif"> 15. Mimi has seven books from the Statistics is Enjoyable sequence. She plans on bringing three of the seven books with her in a street journey. What number of other ways can the three books be chosen? (5 pts) .gif">.gif">.gif">.gif">.gif"> Questions 16 and 17 contain the random variable x with chance distribution given beneath. Present all work. Simply the reply, with out supporting work, will obtain no credit score. x -1 zero 1 2 P( x) zero.1 zero.three zero.four zero.2 16. Decide the anticipated worth of x. (5 pts) 17. Decide the usual deviation of x. (Spherical the reply to 2 decimal locations) (10 pts) .gif">.gif">.gif">.gif">.gif"> Contemplate the next state of affairs for Questions 18, 19 and 20. Present all work. Simply the reply, with out supporting work, will obtain no credit score. Mimi simply began her tennis class three weeks in the past. On common, she is ready to return 20% of her opponent’s serves. Assume her opponent serves eight instances. 18. Let X be the variety of returns that Mimi will get. As we all know, the distribution of X is a binomial chance distribution. What's the variety of trials (n), chance of successes (p) and chance of failures (q), respectively? (5 pts) STAT200 : Introduction to Statistics Last Examination, Fall 2014 OL4 / US2 Web page four of 6 19. Discover the chance that that she returns not less than 1 of the eight serves from her opponent. (10 pts) 20. What number of serves can she anticipate to return? (5 pts) .gif">.gif">.gif">.gif"> Confer with the next data for Questions 21, 22, and 23. Present all work. Simply the reply, with out supporting work, will obtain no credit score. The heights of dogwood timber are usually distributed with a imply of 9 toes and a typical deviation of three toes. 21. What's the chance that a randomly chosen dogwood tree is bigger than 12 toes? (5 pts) 22. Discover the 75th percentile of the dogwood tree peak distribution. (10 pts) 23. If a random pattern of 36 dogwood timber is chosen, what's the chance that the imply peak of this pattern is lower than 10 toes? (10 pts) .gif">.gif">.gif">.gif">.gif"> 24.A random pattern of 100 mild bulbs has a imply lifetime of 3000 hours. Assume that thepopulation customary deviation of the lifetime is 500 hours. Assemble a 95% confidence interval estimate of the imply lifetime. Present all work. Simply the reply, with out supporting work, will obtain no credit score.(15 pts) .gif">.gif">.gif">.gif"> 25. Given a pattern measurement of 100, with pattern imply 730 and pattern customary deviation 100, we carry out the next speculation check on the a = zero.05 stage. H0 : m=750 H1: m¹750 (a) Decide the check statistic. Present all work; writing the right check statistic, with out supporting work, will obtain no credit score. (b) Decide the vital values. Present all work; writing the right vital worth, with out supporting work, will obtain no credit score. (c) What's your conclusion of the check? Please clarify. (20 pts) .gif">.gif">.gif">.gif"> 26. Contemplate the speculation check given by H0 : p=zero.5 H1: p<0.5 In a random sample of 225 subjects, the sample proportion is found to be pˆ = 0.51. (a) Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit. STAT200 : Introduction to Statistics Final Examination, Fall 2014 OL4 / US2 Page 5 of 6 (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 the a = 0.01 level? Explain. (20 pts) .gif">.gif">.gif">.gif"> 27. In a research of reminiscence recall, 5 individuals got 10 minutes to memorize an inventory of 20 phrases. Every was requested to record as most of the phrases as she or he might bear in mind each 1 hour and 24 hours later. The result's proven within the following desk. Variety of Phrases Recalled Topic 1 hour later 24 hours later 1 14 12 2 18 15 three 11 9 four 13 12 5 12 12 Is there proof to counsel that the imply variety of phrases recalled after 1 hour exceeds the imply recall after 24 hours? Assume we wish to use a zero.01 significance stage to check the declare. (a) Establish the null speculation and the choice speculation. (b) Decide the check statistic. Present all work; writing the right check statistic, with out supporting work, will obtain no credit score. (c) Decide the vital worth. Present all work; writing the right vital worth, with out supporting work, will obtain no credit score. (d) Is there enough proof to assist the declare that the imply variety of phrases recalled after 1 hour exceeds the imply recall after 24 hours? Justify your conclusion. (20 pts) .gif">.gif">.gif">.gif">.gif"> Confer with the next information for Questions 28 and 29. x zero -1 three 5 y three -2 three eight 28. Discover an equation of the least squares regression line. Present all work; writing the right equation, with out supporting work, will obtain no credit score. (15 pts) 29. Primarily based on the equation from # 28, what's the predicted worth of y if x = four? Present all work and justify your reply. (5 pts) .gif">.gif">.gif">.gif"> STAT200 : Introduction to Statistics Last Examination, Fall 2014 OL4 / US2 Web page 6 of 6 30. The UMUC MiniMart sells 4 several types of teddy bears. The supervisor stories that the 4 sorts are equally standard. Suppose that a pattern of 100 purchases yields noticed counts 30, 24, 22, and 24 for sorts 1, 2, three, and four, respectively. Kind 1 2 three four Quantity 30 24 22 24 Assume we wish to use a zero.10 significance stage to check the declare that the 4 sorts are equally standard. (a) Establish the null speculation and the choice speculation. (b) Decide the check statistic. Present all work; writing the right check statistic, with out supporting work, will obtain no credit score. (c) Decide the vital worth. Present all work; writing the right vital worth, with out supporting work, will obtain no credit score. (d) Is there enough proof to assist the manager’s declare that the 4 sorts are equally standard? Justify your reply. (20 pts)