STAT 200 OL4/US2 Sections Final Exam | First 15 solution

STAT 200: Introduction to Statistics Final Examination
STAT 200 OL4/US2 Sections Final Exam Fall 2015

The final exam will be posted at 12:01 am on December 11, and it is due at 11:59 pm on December 13, 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 200 total points.
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.
STAT 200: Introduction to Statistics Final Examination, Fall 2015 OL4/US2 Page 2 of 6
1. True or False. Justify for full credit. (15 pts)
(a) If the variance of a data set is zero, then all the observations in this data set are zero.
(b) If P(A) = 0.4 , P(B) = 0.5, and A and B are disjoint, then P(A AND B) = 0.9.
(c) Assume X follows a continuous distribution which is symmetric about 0. If , then .
(d) A 95% confidence interval is wider than a 90% confidence interval of the same parameter.
(e) In a right-tailed test, the value of the test statistic is 1.5. If we know the test statistic follows a Student’s t-distribution with P(T < 1.5) = 0.96, then we fail to reject the null hypothesis at 0.05 level of significance .
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
Relative Frequency
1.0 - 1.9
3
2.0 - 2.9
12
3.0 - 3.9
0.20
4.0 - 4.9
3
5.0 -5.9
Total
25
2. Complete the frequency table with frequency and relative frequency. Express the relative frequency to two decimal places. (5 pts)
3. What percentage of the checkout times was at least 3 minutes? (3 pts)
4. In what class interval must the median lie? Explain your answer. (5 pts)
5. Does this distribution have positive skew or negative skew? Why? (2 pts)
Refer to the following information for Questions 6 and 7. 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. (Note: There are 4 aces in a deck of cards)
6. 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) (5 pts)
STAT 200: Introduction to Statistics Final Examination, Fall 2015 OL4/US2 Page 3 of 6
7. 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) (5 pts)
Refer to the following situation for Questions 8, 9, and 10.
The five-number summary below shows the grade distribution of two STAT 200 quizzes for a sample of 500 students.
Minimum
Q1
Median
Q3
Maximum
Quiz 1
15
30
55
85
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. (4 pts each)
8. Which quiz has less interquartile range in grade distribution?
9. Which quiz has the greater percentage of students with grades 80 or over?
10. Which quiz has a greater percentage of students with grades less than or equal to 50?
Refer to the following information for Questions 11, 12, and 13. Show all work. Just the answer, without supporting work, will receive no credit.
There are 1000 students in a high school. Among the 1000 students, 800 students have a laptop, and 300 students have a tablet. 250 students have both devices.
11. What is the probability that a randomly selected student has neither device? (10 pts)
12. What is the probability that a randomly selected student has a tablet, given that he/she has a laptop? (5 pts)
13. Let event A be the selected student having a laptop, and event B be the selected student having a tablet. Are A and B independent events? Why or why not? (5 pts)
14. A combination lock uses three distinctive numbers between 0 and 39 inclusive. How many different ways can a sequence of three numbers be selected? (Show work) (5 pts)
15. Let random variable x represent the number of heads when a fair coin is tossed three times. Show all work. Just the answer, without supporting work, will receive no credit.
(a) Construct a table describing the probability distribution. (5 pts)
(b) Determine the mean and standard deviation of x. (Round the answer to two decimal places) (10 pts)