STAT 200 OL1/US1 Sections Final Exam Spring 2018

STAT 200: Introduction to Statistics Final Examination, Spring 2018 OL1 Page 1 of 7
STAT 200
OL1/US1 Sections
Final Exam
Spring 2018
The final exam will be posted at 12:01 am on March 2, and it is
due at 11:59 pm on March 4, 2018. Eastern Time is our reference
time.
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 handheld 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 200 total points; 10 points 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, Spring 2018 OL1 Page 2 of 7
1. True or False. Justify for full credit.
(a) If P(A) = 0.4, P(B) = 0.5, and A and B are independent, then P(A AND B) = 0.9.
(b) If the variance of a data set is 0, then all the observations in this data set must be zero.
(c) The mean is always equal to the median for a normal distribution.
(d) A 95% confidence interval is wider than a 90% confidence interval of the same parameter.
(e) In a two-tailed test, the value of one 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) Among the Senators in the current Congress, 54% are Republicans. The value 54% is a
(i) statistic

(ii)
(iii) parameter
cannot be determined

(b) The hotel ratings are usually on a scale from 0 star to 5 stars. The level of this measurement is

(i)
(ii)
(iii)
(iv) interval
nominal
ordinal
ratio

(c) In a career readiness research, 100 students were randomly selected from the psychology
program, 150 students were randomly selected from the communications program, and 120
students were randomly selected from cyber security program. This type of sampling is called:

(i)
(ii)
(iii)
(iv) cluster
convenience
systematic
stratified

STAT 200: Introduction to Statistics Final Examination, Spring 2018 OL1 Page 3 of 7
3. Choose the best answer. Justify for full credit.
(a) A study of 10 different weight loss programs involved 500 subjects. Each of the 10 programs
had 50 subjects in it. The subjects were followed for 12 months. Weight change for each
subject was recorded. You want to test the claim that the mean weight loss is the same for the
10 programs. What statistical approach should be used?

(i)
(ii)
(iii)
(iv) t-test
linear regression
ANOVA
confidence interval

(b) A STAT 200 instructor teaches two classes. She wants to test if the variances of the score
distribution for the two classes are different. What type of hypothesis test should she use?

(i)
(ii)
(iii)
(iv) t-test for two independent samples
t-test for matched samples
z-test for two samples
F- test

4. The frequency distribution below shows the distribution for IQ scores for a random sample of
1000 adults. (Show all work. Just the answer, without supporting work, will receive no credit.)

IQ Scores Frequency Relative Frequency

50 - 69 24

70 - 89

90 -109 453

110 - 129 0.25

130 - 149 25

Total 1000

(a) Complete the frequency table with frequency and relative frequency. Express the relative
frequency to three decimal places.
(b) What percentage of the adults in this sample has an IQ score of at least 110?
(c) Does this distribution have positive skew or negative skew? Why or why not?
STAT 200: Introduction to Statistics Final Examination, Spring 2018 OL1 Page 4 of 7
5. 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 35 55 85 100

Quiz 2 20 35 50 90 100

For each question, give your answer as one of the following: (i) Quiz 1; (ii) Quiz 2; (iii) Both quizzes
have the same value requested; (iv) It is impossible to tell based on the given information. Then
explain your answer in each case.

(a)
(b)
(c) Which quiz has less range in grade distribution?
Which quiz has the greater percentage of students with grades 85 and over?
Which quiz has a greater percentage of students with grades less than 60?

6. A sample of 10 LED light bulbs consists of 1 defective and 9 good light bulbs. A quality
control technician wants to randomly select two of the light bulbs for inspection. Find the
probability that the first selected light bulb is good and the second light bulb is also good.
(Show all work. Just the answer, without supporting work, will receive no credit.)
(a) Assuming the two random selections are made with replacement.
(b) Assuming the two random selections are made without replacement.
7. There are 1000 students in a high school. Among the 1000 students, 250 students take AP
Statistics, and 300 students take AP French. 100 students take both AP courses. Let S be the
event that a randomly selected student takes AP Statistics, and F be the event that a randomly
selected student takes AP French. 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 F).
(b) What is the probability of complement event of (S OR F)?
8. Consider rolling two fair dice. Let A be the event that the sum of the two dice is 8, and B be
the event that the first one is a multiple of 3.
(a) What is the probability that the sum of the two dice is 8 given that the first one is a multiple of
3? Show all work. Just the answer, without supporting work, will receive no credit.
(b) Are event A and event B independent? Explain.
STAT 200: Introduction to Statistics Final Examination, Spring 2018 OL1 Page 5 of 7
9. Answer the following two questions. (Show all work. Just the answer, without supporting
work, will receive no credit).
(a) UMUC Stat Club is sending a delegate of 2 members to attend the 2018 Joint Statistical
Meeting in Vancouver, Canada. There are 10 qualified candidates. How many different ways
can the delegate be selected?
(b) A bike courier needs to make deliveries at 6 different locations. How many different routes can
he take?
10. Assume random variable x follows a probability distribution shown in the table below.
Determine the mean and standard deviation of x. Show all work. Just the answer, without
supporting work, will receive no credit.

x -2 0 1 2 3

P(x) 0.1 0.1 0.4 0.2 0.2

11. Mimi is into figure skating these days due to the Winter Olympics. She started learning toe loop
jumps a couple weeks ago. Her probability of landing a successful single toe loop jump is 0.30.
She plans to attempt 10 single toe loop jumps in her practice session tomorrow.
(a) Let X be the number of successful single toe loop jumps that Mimi lands. 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 lands at least one successful single toe loop jump in her 10
attempts. (round the answer to 3 decimal places) Show all work. Just the answer, without
supporting work, will receive no credit.
12. Assume the weights of men are normally distributed with a mean of 170 lbs and a standard
deviation of 30 lbs. Show all work. Just the answer, without supporting work, will receive no
credit.
(a) Find the 75th percentile for the distribution of men’s weights.
(b) What is the probability that a randomly selected man weighs more than 200 lbs?
13. 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) If a random sample of 64 test scores is selected, what is the standard deviation of the sample
mean?
(b) What is the probability that 64 randomly selected test scores will have a mean test score that is
between 475 and 525?
STAT 200: Introduction to Statistics Final Examination, Spring 2018 OL1 Page 6 of 7
14. A survey showed that 80% of the 1600 adult respondents believe in global warming. Construct a
90% confidence interval estimate of the proportion of adults believing in global warming. Show
all work. Just the answer, without supporting work, will receive no credit.
15. In a study designed to test the effectiveness of garlic for lowering cholesterol, 49 adults were
treated with garlic tablets. Cholesterol levels were measured before and after the treatment. The
changes in their LDL cholesterol (in mg/dL) have a mean of 3 and standard deviation of 14.
Construct a 95% confidence interval estimate of the mean change in LDL cholesterol after the
garlic tablet treatment. Show all work. Just the answer, without supporting work, will receive
no credit.
16. Mimi is interested in testing the claim that banana is the favorite fruit for more than 80% of the
adults. She conducted a survey on a random sample of 100 adults. 85 adults in the sample
chose banana as his / her favorite fruit.
Assume Mimi 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 banana is the favorite fruit for more than
80% of the adults? Explain.
17. In a study of freshman weight gain, the measured weights of 5 randomly selected college
students in September and April of their freshman year are shown in the following table.

Weight (lb)

Student September April

1 147 150

2 127 125

3 140 150

4 156 160

5 154 156

Is there evidence to suggest that the mean weight of the freshmen in April is greater than the
mean weight in September?
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 for this test. Show all work; writing the correct P-value, without
supporting work, will receive no credit.
STAT 200: Introduction to Statistics Final Examination, Spring 2018 OL1 Page 7 of 7
(d) Is there sufficient evidence to support the claim that the mean weight of the freshmen in April
is greater than the mean weight in September? Justify your conclusion.
18. In a pulse rate research, a simple random sample of 40 men results in a mean of 80 beats per
minute, and a standard deviation of 11.3 beats per minute. Based on the sample results, the
researcher concludes that the pulse rates of men have a standard deviation greater than 10 beats
per minutes. Use a 0.05 significance level to test the researcher’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 the researcher’s claim? Explain.
19. 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 35 25 16 10 14

(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.
20. A STAT 200 instructor believes that the average quiz score is a good predictor of final exam
score. A random sample of 8 students produced the following data where x is the average quiz
score and y is the final exam score.

x 85 50 72 65 78 60 100 70

y 85 75 75 64 80 65 95 60

(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.