STAT 200: Introduction to Statistics Final Examination, Fall 2017 OL4
STAT 200 OL4/US2 Sections Final Exam
The final exam will be posted at 12:01 am on December 15, and it is due at 11:59 pm on December 17, 2017. 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 hand- held calculators, statistical packages) to aid in your calculation, you must cite the sources and explain how you get the results. You can only submit the Word doc answer sheet. Final Exam answer sheets must be uploaded before the deadline as they will not be accepted via email.
Record your answers and work on the separate Word doc 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 OL4
True or False. Justify for full credit.
Choose the best answer. Justify for full credit.
UMUC STAT Club wanted to estimate the study hours of STAT 200 students. One STAT 200 section was randomly selected and all students from that section were asked to fill out the questionnaire. This type of sampling is called:
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) (ii) (iii) (iv)
cluster convenience systematic stratified
STAT 200: Introduction to Statistics Final Examination, Fall 2017 OL4 Page 3 of 9
The hotel ratings are usually on a scale from 0 star to 5 stars. The level of this measurement is
500 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?
You choose an alpha level of 0.01 and then analyze your data. What is the probability that you will make a Type I error given that the null hypothesis is true?
A random sample of 500 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)
0.0 – 5.0
5.1 – 10.0
10.1 – 15.0
15.1 – 20.0
20.1 – 25.0
Complete the frequency table with frequency and relative frequency. Express the relative frequency to two decimal places.
What percentage of the study times was not more than 15 hours?
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?
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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) (b) (c) (d) (e)
What is the minimum in the grade distribution?
Which quarter has the smallest spread of data? What is that spread?
Find the interquartile range in the grade distribution.
Are there more students in the score band of 45- 65 or 65 – 85? Why?
Can the average score be determined based on the given information? Why or why not?
A basket contains 1 white balls, 5 yellow balls, and 4 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.)
Assuming the ball selection is without replacement. What is the probability that the first ball is white and the second ball is red?
Assuming the ball selection is with replacement. What is the probability that the first ball is red and the second ball is also red?
There are 1000 juniors in a college. Among the 1000 juniors, 400 students are taking STAT200, and 700 students are taking PSYC300. There are 200 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.)
Provide a written description of the complement event of (S OR P). What is the probability of complement event of (S OR P)?
STAT 200: Introduction to Statistics Final Examination, Fall 2017 OL4 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 equal to 7, and B be the event that the first one is an odd number.
8. Answer the following two questions. (Show all work. Just the answer, without supporting work, will receive no credit).
9. Imagine you are in a game show. There are 20 prizes hidden on a game board with 100 spaces. One prize is worth $50, nine are worth $20, and another ten are worth $10. You have to pay $5 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.
10. Mimi joined UMUC basketball team in spring 2017. On average, she is able to score 20% of the field goals. Assume she tries 10 field goals in a game.
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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 2.5 hours. Show all work. Just the answer, without supporting work, will receive no credit.
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.
STAT 200: Introduction to Statistics Final Examination, Fall 2017 OL4 Page 7 of 9
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
1 hour later 24 hours later
1 2 3 4 5
13 13 18 14 12 11 15 14 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.
Identify the null hypothesis and the alternative hypothesis.
Determine the test statistic. Show all work; writing the correct test statistic, without supporting
work, will receive no credit.
Determine the P-value. Show all work; writing the correct P-value, without supporting work, will receive no credit.
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.
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 400 bottles yielded a mean of 357.2 ml and a standard deviation of 16.2 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 0.05 significance level to test John’s claim.
Identify the null hypothesis and alternative hypothesis.
Determine the test statistic. Show all work; writing the correct test statistic, without supporting work, will receive no credit.
Determine the P-value for this test. Show all work; writing the correct P-value, without supporting work, will receive no credit.
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.
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18. The UMUC Daily News reported that the color distribution for plain M&M’s was: 35% brown, 30% yellow, 15% orange, 10% green, and 10% tan. Each piece of candy in a random sample of 200 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.
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.
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20. A study of 10 different weight loss programs involved 200 subjects. Each of the 10 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 10 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
Degrees of Freedom
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