Mathematics – Statistics
This is an open-book exam. You may refer to your text and other course materials
for the current course 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. It is a violation of the UMUC Academic Dishonesty and
Plagiarism policy to use unauthorized materials or work from others.
Answer all 20 questions. Make sure your answers are as complete as possible.
Show all of your supporting work and reasoning. Answers that come straight
from calculators, programs or software packages without any explanation will not
be accepted. If you need to use technology (for example, Excel, online or hand-
held calculators, statistical packages) to aid in your calculation, you must cite the
sources and explain how you get the results.
Record your answers and work on the separate answer sheet provided.
This exam has 20 questions; 5% for each question.
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 2017 OL1 Page 2 of 9
1. True or False. Justify for full credit.
(a) If A and B are disjoint, P(A) = 0.4 and P(B) = 0.5, then P(A AND B) = 0.2.
(b) If all the observations in a data set are identical, then the variance for this data set is zero.
(c) There may be more than one mode in a data set.
(d) A 95% confidence interval is wider than a 98% confidence interval of the same parameter.
(e) In a two-tailed test, the value of the test statistic is 2. The test statistic follows a
distribution with the distribution curve shown below. If we know the shaded area is 0.03,
then we have sufficient evidence to reject the null hypothesis at 0.05 level of significance.
2. Choose the best answer. Justify for full credit.
(a) The quality control department of a semiconductor manufacturing company tests every 100th
product from the assembly line. This type of sampling is called:
(i) cluster
(ii) convenience
(iii) systematic
(iv) stratified
(b) A study was conducted at a local college to analyze the trend of average GPA of all students
graduated from the college. According to the Registrar, the average GPA for students with
economics major from the class of 2016 is 3.5. The value 3.5 is a
(i) statistic
(ii) parameter
(iii) cannot be determined
(c) The hotel ratings are usually on a scale from 0 star to 5 stars. The level of this measurement is
STAT 200: Introduction to Statistics Final Examination, Fall 2017 OL1 Page 3 of 9
(i) interval
(ii) nominal
(iii) ordinal
(iv) ratio
(d) 600 students took a chemistry test. You sampled 100 students to estimate the average score and the standard deviation. How many degrees of freedom were there in the estimation of the
standard deviation?
(i) 599 (ii) 600 (iii) 99 (iv) 100
(e) You choose an alpha level of 0.05 and then analyze your data. What is the probability that you will make a Type I error given that the null hypothesis is true?
(i) 0.01 (ii) 0.025 (iii) 0.05 (iv) 0.10
3. A random sample of 200 students was chosen from UMUC STAT 200 classes. The frequency
distribution below shows the distribution for study time each week (in hours). (Show all work.
Just the answer, without supporting work, will receive no credit.)
Study Time (in hours) Frequency Relative Frequency
0.0 – 5.0 6
5.1 – 10.0 24
10.1 – 15.0 50
15.1 – 20.0 0.35
20.1 – 25.0
Total 200
(a) Complete the frequency table with frequency and relative frequency. Express the relative
frequency to two decimal places.
(b) What percentage of the study times was at most 15 hours?
(c) In what class interval must the median lie? 5.1 – 10.0, 10.1 -15.0, 15.1 – 20.0, or 20.1 – 25.0?
Why?
STAT 200: Introduction to Statistics Final Examination, Fall 2017 OL1 Page 4 of 9
4. The five-number summary below shows the grade distribution of a STAT 200 quiz for a
sample of 500 students.
Answer each question based on the given information, and explain your answer in each case.
(a) What is the minimum in the grade distribution?
(b) Which quarter has the smallest spread of data? What is that spread?
(c) Find the interquartile range (IQR) in the grade distribution.
(d) Are there more students in the score band of 20 – 40 or 60 – 80? Why?
(e) Can the average score be determined based on the given information? Why or why not?
5. A basket contains 2 white balls, 5 yellow balls, and 3 red balls. Consider selecting one ball at a
time from the basket. (Show all work. Just the answer, without supporting work, will receive
no credit.)
(a) Assuming the ball selection is with replacement. What is the probability that the first ball is red
and the second ball is yellow?
(b) Assuming the ball selection is without replacement. What is the probability that the first ball is
red and the second ball is also red?
6. There are 1500 juniors in a college. Among the 1500 juniors, 600 students are taking
STAT200, and 800 students are taking PSYC300. There are 500 students taking both courses.
Let S be the event that a randomly selected student takes STAT200, and P be the event that a
randomly selected student takes PSYC300. (Show all work. Just the answer, without
supporting work, will receive no credit.)
(a) Provide a written description of the complement event of (S OR P).
(b) What is the probability of complement event of (S OR P)?
STAT 200: Introduction to Statistics Final Examination, Fall 2017 OL1 Page 5 of 9
7. Consider rolling a fair 6-faced die twice. Let A be the event that the sum of the two rolls is at
most 4, and B be the event that the first one is an odd number.
(a) What is the probability that the sum of the two rolls is at most 4 given that the first one is an
odd number? Show all work. Just the answer, without supporting work, will receive no credit.
(b) Are event A and event B independent? Explain.
8. Answer the following two questions. (Show all work. Just the answer, without supporting
work, will receive no credit).
(a) 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?
(b) A combination lock uses three distinctive numbers between 0 and 49 inclusive. How many
different ways can the sequence of three numbers be selected?
9. Imagine you are in a game show. There are 30 prizes hidden on a game board with 100 spaces.
One prize is worth $100, nine are worth $50, and another twenty are worth $10. You have to
pay $10 to the host if your choice is not correct. Let the random variable x be the money you
get or lose. Show all work. Just the answer, without supporting work, will receive no credit.
(a) Complete the following probability distribution.
x P(x)
-$10
$10
$50
$100
(b) What is your expected winning or loss in this game? Be specific in your answer whether it’s
winning or loss.
10. Mimi joined UMUC basketball team in spring 2017. On average, she is able to score 30% of the field
goals. Assume she tries 15 field goals in a game.
(a) Let X be the number of field goals that Mimi scores in the game. 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?
(b) Find the probability that Mimi scores at least 3 of the 15 field goals. (round the answer to 3 decimal
places) Show all work. Just the answer, without supporting work, will receive no credit.
STAT 200: Introduction to Statistics Final Examination, Fall 2017 OL1 Page 6 of 9
11. A research concludes that the number of hours of exercise per week for adults is normally
distributed with a mean of 4 hours and a standard deviation of 3 hours. Show all work. Just the
answer, without supporting work, will receive no credit.
(a) What is the probability that a randomly selected adult has more than 7 hours of exercise per week
(round the answer to 4 decimal places)
(b) Find the 80th percentile for the distribution of exercise time per week. (round the answer to 2 decimal
places)
12. Assume the SAT Mathematics Level 2 test scores are normally distributed with a mean of 500
and a standard deviation of 100. Show all work. Just the answer, without supporting work, will
receive no credit.
(a) Consider all random samples of 64 test scores. What is the standard deviation of the sample
means? (Round your answer to three decimal places)
(b) What is the probability that 64 randomly selected test scores will have a mean test score that is
greater than 525? (Round your answer to four decimal places)
13. A city built a new parking garage in a business district. For a random sample of 100 days, daily
fees collected averaged $2,500, with a standard deviation of $500. Construct a 90% confidence
interval estimate of the mean daily income this parking garage generates. Show all work. Just
the answer, without supporting work, will receive no credit.
14. Mimi conducted a survey on a random sample of 100 adults. 70 adults in the sample chose
banana as his / her favorite fruit. Construct a 95% confidence interval estimate of the proportion
of adults whose favorite fruit is banana. Show all work. Just the answer, without supporting
work, will receive no credit.
15. A researcher is interested in testing the claim that more than 75% of the adults believe in
global warming. She conducted a survey on a random sample of 400 adults. The survey
showed that 320 adults in the sample believe in global warming.
Assume the researcher wants to use a 0.05 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 P-value for this test. Show all work; writing the correct P-value, without
supporting work, will receive no credit.
(d) Is there sufficient evidence to support the claim that more than 75% of adults believe in global
warming? Explain.
STAT 200: Introduction to Statistics Final Examination, Fall 2017 OL1 Page 7 of 9
16. 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 13 12
2 18 16
3 10 9
4 15 13
5 11 11
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 0.05 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 P-value. Show all work; writing the correct P-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.
17. John oversees a bottle-filling machine in a company. The amount of fluid dispensed into each
bottle is approximately normally distributed with an unknown population standard deviation.
On a particular day, a random sample of 50 bottles yielded a mean of 357.2 ml and a standard
deviation of 15.8 ml. John then concluded that the population standard deviation of the fluid
dispense amount by the machine is greater than 15 ml.
The lead engineer wants to use a 0.01 significance level to test John’s claim.
(a) Identify the null hypothesis and 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 P-value for this test. Show all work; writing the correct P-value, without
supporting work, will receive no credit.
(d) Is there sufficient evidence to support John’s claim that the population standard deviation
of the fluid dispense amount by the machine is greater than 15 ml? Explain.
STAT 200: Introduction to Statistics Final Examination, Fall 2017 OL1 Page 8 of 9
18. The UMUC Daily News reported that the color distribution for plain M&M’s was: 40%
brown, 20% yellow, 20% orange, 10% green, and 10% tan. Each piece of candy in a random
sample of 100 plain M&M’s was classified according to color, and the results are listed below.
Use a 0.05 significance level to test the claim that the published color distribution is correct.
Show all work and justify your answer.
Color Brown Yellow Orange Green Tan
Number 42 21 12 7 18
(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 P-value. Show all work; writing the correct P- value, without supporting work,
will receive no credit.
(d) Is there sufficient evidence to support the claim that the published color distribution is correct?
Justify your answer.
19. A STAT 200 instructor believes that the average quiz score is a good predictor of final exam
score. A random sample of 10 students produced the following data where x is the average quiz
score and y is the final exam score.
x 72 94 55 63 100 40 85 70 75 85
y 70 96 50 70 96 50 83 75 77 87
(a) Find an equation of the least squares regression line. Show all work; writing the correct
equation, without supporting work, will receive no credit.
(b) Based on the equation from part (a), what is the predicted final exam score if the average quiz
score is 80? Show all work and justify your answer.
20. A study of 15 different weight loss programs involved 300 subjects. Each of the 15 programs
had 20 subjects in it. The subjects were followed for 12 months. Weight change for each subject was
recorded. We want to test the claim that the mean weight loss is the same for the 15 programs.
(a) Complete the following ANOVA table with sum of squares, degrees of freedom, and mean
square (Show all work):
Source of Variation Sum of Squares
(SS)
Degrees of Freedom
(df)
Mean Square
(MS)
Factor
(Between) 42.5
Error
(Within)
Total 553.05 299 N/A
STAT 200: Introduction to Statistics Final Examination, Fall 2017 OL1 Page 9 of 9
(b) Determine the test statistic. Show all work; writing the correct test statistic, without supporting
work, will receive no credit.
(c) Determine the P-value. Show all work; writing the correct P-value, without supporting work,
will receive no credit.
(d) Is there sufficient evidence to support the claim that the mean weight loss is the same for the 15
programs at the significance level of 0.10? Explain.
