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Question Details:
#6141

STAT 200 Final exam solution correct answers

*STAT 200*

*O**L**4 / US2 Sections*

*Final Exam*

*Spring 2015*

**The final exam will be posted at 12:01 am on May 8, and it is due at 11:59 pm on May 10, 2015. Eastern Time is our reference time.**

**This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator. You must complete the exam individually. Neither collaboration nor consultation with others is allowed.**

**Answer all 25 questions. Make sure your answers are as complete as possible. Show all of your work and reasoning. In particular, when there are calculations involved, you must show how you come up with your answers with critical work and/or necessary tables. Answers that come straight from programs or software packages will not be accepted. If you need to use software (for example, Excel) and /or online or hand-held calculators to aid in your calculation, please cite the sources and explain how you get the results.**

**Record your answers and work on the separate answer sheet provided. ****This exam has 250 total points.**

*Y**ou 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)

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

1

(b)

*P*( *A *AND *A**c *)

, where *A**c *is the complement of *A*.

(c) The mean is always equal to the median for a normal distribution.

(d) A 99% confidence interval is wider than a 95% confidence interval of the same parameter.

(e) 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**

**P****M 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)

**5. **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 remain

the 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)

**7. **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)

**8. **Are *A *and *B *independent? Why or why not? (5 pts)

Refer to the following situation for Questions 9, 10, and 11.

**T****he 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

**F****or 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)

**9. **Which quiz has less interquartile range in grade distribution?

**10. **Which quiz has the greater percentage of students with grades 90 and over?

**11. **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.*

**T****here 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.**

**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)

Solution Details:
#6144

STAT 200 Introduction to Statistics Name______________________________
Final Examination: Spring 2015 OL4 / US2 Instructor __________________________
Answer Sheet
Instructions:
This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator.
Record your answers and work in this document.
Answer all 25 questions. Make sure your answers are as complete as possible. Show all of your work and reasoning. In particular, when there are calculations involved, you must show how you come up with your answers with critical work and/or necessary tables. Answers that come straight from programs or software packages will not be accepted. If you need to use software (for example, Excel) and /or online or hand-held calculators to aid in your calculation, please cite the source and explain how you get the results.
When requested, show all work and write all answers in the spaces allotted on the following pages. You may type your work using plain-text formatting or an equation editor, or you may hand-write your work and scan it. In either case, show work neatly and correctly, following standard mathematical conventions. Each step should follow clearly and completely from the previous step. If necessary, you may attach extra pages.
You must complete the exam individually. Neither collaboration nor consultation with others is allowed. Your exam will receive a zero grade unless you complete the following honor statement.
Record your answers and work.
Problem Number Solution
1
(25 pts) Answers:
(a) True
(b) False
(c) True
(d) True
(e) False
Work for (a), (b), (c), (d) and (e):
Variance represents the average of the squared difference from the mean. Variance 0 means all values are same as mean which indicates identical values. Thus the statement is true.
As there is no common region between A and Ac so P(A and Ac) = 0 and thus the given statement is false.
As the normal distribution is symmetric about the mean so the mean and median is the same value and thus the given statement is true.
For 99% confidence interval we need a larger Z or t-value (or any other value as appropriate) to multiply with standard error to find out the confidence interval. Thus the statement is correct.
Smaller significance level gives larger ...

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