# STAT 230 OL4 / US2 Sections Final Exam Spring 2015 | Complete Solution - 90857

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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. 1. True or False. Justify for full credit. (25 pts) If the variance from a data set is zero, then all the observations in this data set must be identical. (b) P(A AND Ac ) 1, where Ac is the complement of A. The mean is always equal to the median for a normal distribution. A 99% confidence interval is wider than a 95% confidence interval of the same parameter. It is easier to reject the null hypothesis if we use a smaller significance level ?. 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. A random sample of 25 customers was chosen in UMUC MiniMart between 3:00 and 4:00 PM on a Friday afternoon. The frequency distribution below shows the distribution for checkout time (in minutes). Checkout Time (in minutes) Frequency Relative Frequency 1.0 - 1.9 4 2.0 - 2.9 0.4 3.0 - 3.9 4.0 - 4.9 5 Total 25 2. Complete the frequency table with frequency and relative frequency. (5 pts) 3. What percentage of the checkout times was at least 3 minutes? (5 pts) 4. In what class interval must the median lie? Explain your answer. (5 pts) Assume that the largest observation in this dataset is 4.8. Suppose this observation were incorrectly recorded as 8.4 instead of 4.8. Will the mean increase, decrease, or remainthe same? Will the median increase, decrease or remain the same? Why? (5 pts) Refer to the following information for Questions 6, 7, and 8. Show all work. Just the answer, without supporting work, will receive no credit. A 6-faced die is rolled two times. Let A be the event that the outcome of the first roll is an even number, and B be the event that the outcome of second roll is greater than 4. 6. How many outcomes are there in the sample space? (5 pts) What is the probability that the outcome of the second roll is greater than 4, given that the first roll is an even number? (10 pts) STAT 230 Introductory Business Statistics Final Examination Spring 2015 OL4/US2 Page 3 of 6 8. Are A and B independent? Why or why not? (5 pts) Refer to the following situation for Questions 9, 10, and 11. The five-number summary below shows the grade distribution of two STAT 200 quizzes. Minimum Q1 Median Q3 Maximum Quiz 1 12 40 60 95 100 Quiz 2 20 35 50 90 100 For each question, give your answer as one of the following: (a) Quiz 1; (b) Quiz 2; (c) Both quizzes have the same value requested; (d) It is impossible to tell using only the given information. Then explain your answer in each case. (5 pts each) Which quiz has less interquartile range in grade distribution? Which quiz has the greater percentage of students with grades 90 and over? Which quiz has a greater percentage of students with grades less than 60? 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 in the STAT200 roster, and 100 students are in the PSYC300 roster. There are 80 students taking both courses. What is the probability that a randomly selected junior is taking at least one of these two courses? (10 pts) What is the probability that a randomly selected junior is taking PSYC300, given that he/she is taking STAT200? (10 pts) UMUC Stat Club is selecting three officers for the school year - a president, a vice president and a treasurer. There are 10 qualified candidates. How many different ways can the officers be selected? Show all work. Just the answer, without supporting work, will receive no credit.(5 pts) 15. Imagine you are in a game show. There are 6 prizes hidden on a game board with 10 spaces. One prize is worth \$100, another is worth \$20, and four are worth \$5.You have to pay \$20 to the host if your choice is not correct. Let the random variable x be the winning. Show all work. Just the answer, without supporting work, will receive no credit. STAT 230 Introductory Business Statistics Final Examination Spring 2015 OL4/US2 Page 4 of 6 (a) What is your expected winning in this game? (5 pts) (b) Determine the standard deviation of x. (Round the answer to two decimal places) (10 pts)
Solution Description

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.

1.         True or False. Justify for full credit.                                                                 (25 pts)

1. If the variance from a data set is zero, then all the observations in this data set must be identical.

(b)  P(A AND Ac )   1, where Ac  is the complement of A.

1. The mean is always equal to the median for a normal distribution.
2. A 99% confidence interval is wider than a 95% confidence interval of the same parameter.
3. It is easier to reject the null hypothesis if we use a smaller significance level α.

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.

A random sample of 25 customers was chosen in UMUC MiniMart between 3:00 and 4:00 PM on a Friday afternoon. The frequency distribution below shows the distribution for checkout time (in minutes).

Checkout Time (in minutes)

Frequency

Relative Frequency

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