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STAT 200 OL4 / OL2 Sections Final Exam Fall 2014

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Question;1. True;or False. Justify for full credit. (25;pts);(a) If;there is no linear correlation between two variables, then these two variables;are not related in any way.;STAT200: Introduction to;Statistics Final Examination, Fall 2014 OL4 /;US2 Page;2 of 6;(b) If;the variance from a data set is zero, then all the observations in this data;set are identical.;(c) P(A;and A)=1, where Ais the;complement of A.;(d) In;a hypothesis testing, if the P-value is less than the significance level?, we;reject the null hypothesis.;(e) The;volume of milk in a jug of milk is 128 oz. The value 128 is from a discrete;data set.;Refer to the following frequency distribution for Questions;2, 3, 4, and 5. 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;2;2.0 - 2.9;12;3.0 - 3.9;2;4.0 - 4.9;4;2.;What percentage of the checkout times was less than 3;minutes?;(5 pts);3.;In what class interval must the median;lie? Explain your answer.;(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);Refer to the following data to answer questions 6, 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;2;15;15;18;40;6.;Find the sample standard deviation. (Round the;answer to two decimal places);(10 pts);7.;Find the coefficient of variation.;(5 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 from a 52-card deck.;Let event A be the first card is an ace, and event B be the second card is an;ace. (Note: There are 4 aces in a deck of cards);STAT200;Introduction to Statistics Final Examination, Fall 2014 OL4;/;US2 Page;3 of 6;9. If;the card selection is without replacement, what is the probability that the;first card is an ace and;the second;card is also an ace? (Express the answer in simplest fraction;form) (10;pts);10. If;the card selection is with replacement, what is the probability that the first;card is an ace and;the;second card is also an ace? (Express the answer in simplest;fraction form);(10 pts);11.;Are A and B independent;when the selection is with replacement? Why or why not?;(5 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 1000 juniors in a college.;Among the 1000 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 taking at least one of;these two;courses? (10;pts);13. What;is the probability that a randomly selected junior is taking PSYC300, given;that;he/she is taking;STAT200? (10;pts);14. UMUC;Stat Club must appoint a president, a vice president, and a treasurer. There;are 10;qualified candidates. How many different ways can the;officers be appointed? (5;pts);15. Mimi;has seven books from the Statistics is Fun series. She plans on bringing three;of the seven;books with;her in a road trip. How many different ways can the three books be;selected? (5 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;P(x);0.1;0.3;0.4;0.2;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 just started her tennis class three weeks ago. On;average, she is able to return 20% of her opponent?s serves. Assume her;opponent serves 8 times.;18. Let;X be the number of returns that Mimi gets. As we know, the distribution of X is;a binomial;probability distribution. What is the number of trials (n);probability of successes (p) and;probability of failures (q);respectively? (5;pts);STAT200: Introduction to;Statistics Final Examination, Fall 2014 OL4 / US2;Page 4 of 6;19.;Find the probability that that she returns at least 1 of;the 8 serves from her opponent.;(10 pts);20.;How many serves can she expect to return?;(5 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 greater than 12 feet?;(5 pts);22.;Find the 75th percentile of the dogwood;tree height distribution.;(10 pts);23. If;a random sample of 36 dogwood trees is selected, what is the probability that;the mean height;of this sample is less than 10;feet? (10;pts);24.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 95% confidence interval estimate of the mean lifetime. 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 a = 0.05;level.;H0: m=750;H1: m?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 values. 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;H0: p=0.5;H1: p<0.5;In a random sample of 225 subjects, the sample proportion is;found to be p? = 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);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;12;2;18;15;3;11;9;4;13;12;5;12;12;Is there evidence to suggest that the mean number of words;recalled after 1 hour exceeds the mean recall after 24 hours?;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? Justify your conclusion.;(20 pts);Refer to;the following data for Questions 28 and 29.;x;0;-1;3;5;y;3;-2;3;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. (5;pts);STAT200: Introduction to Statistics;Final Examination, Fall 2014 OL4 / US2;Page 6 of 6;30.;The UMUC MiniMart sells four different types of teddy;bears. The manager reports that;the four types are equally popular. Suppose that a sample;of 100 purchases yields;observed counts 30, 24, 22, and 24 for types 1, 2, 3, and;4, respectively.;Type;1;2;3;4;Number;30;24;22;24;Assume we want to use a 0.10 significance level to test;the claim that the four types are;equally popular.;(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 manager?s;claim that the four types are;equally popular? Justify your answer.;(20 pts)

 

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