Exam 1 Spring 2023 (4)

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University of South Carolina *

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201

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Statistics

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Jan 9, 2024

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Name: STAT 201 (Murphy) Spring 2023 Version A Exam 1:Chapters 1 – 2 and 5 Directions: Answer each question to the best of your ability. Round all answers to the number of decimals stated in the question. All answers must be in the space provided after the question, partial credit can only be given if you have shown your work. Make sure to include justifications when they are asked for. You may use a calculator and the formula sheet provided but no additional notes. You may not have any paper at your seat other than what is provided to you with this exam. You may not use a computer or a phone (even as a calculator). There is a total of 70 points on this exam. You have only 50 minutes to complete the exam. Good Luck! Note that the data represented in these questions is made up and does not reflect actual data. Use the following to answer questions 1 – 6: A company wants to study their employees that work in their distribution center. A random sample of 18 employees was taken and data was collected from a survey. One of the variables collected was the distance walked during their 8 hour shift. Assume the company provides digital trackers for employees to wear while on shift. Use the data below to answer the questions that following: 1.3 1.5 1.7 1.8 1.9 2.0 2.0 2.1 2.3 2.5 2.5 2.6 2.7 3.0 3.1 3.2 3.7 3.8 Note: ∑ x = ¿ 43.7 and ( x −´ x ) 2 = ¿ ∑ ¿ 10.44. 1. What type of variable is distance walked? a. Categorical b. Discrete Quantitative c. Continuous Quantitative 2. Calculate the sample mean distance walked. (Round your answer to 2 decimal places). 3. Calculate the sample standard deviation. (Round your answer to 2 decimal places). 4. State the five number summary for the sample of data. (Round your answers to 1 decimal place). 5. Since these measurements and results are based on a sample of data (not all employees) they are known as . a. the population. b. statistics. c. parameters. 6. Based on this histogram of the data, what is the shape of the distribution for this sample:

Use the following information to answer questions 7 to 16: A company wants to study their employees that work in their distribution center. A random sample of 100 employees was taken and data was collected from a survey. One of the variables collected was the number of days an employee picked up fast food for their meal during their shift in the last month. The following output was generated using software on the data collected. Sample mean = ´ x = 5.59 Sample standard deviation = s = 4.52 Five Number Summary: Min = 0 Q 1 = 2 Q 2 = Median = 4.5 Q 3 = 8 Max = 22 7. What type of variable is number of days an employee picked up fast food for their meal during their shift in the last month? a. Categorical b. Discrete Quantitative c. Continuous Quantitative 8. Which of the following is the correct description of the population of interest? a. All employees that work in their distribution center. b. The random sample of 100 employees that work in their distribution center. c. The sample mean calculated from the sample of 100 taken. 9. Which value given represents the average distance values fall from the mean? a. 5.59 b. 4.52 c. 2 d. 8 10. Which value given represents the value such that 75% of the data falls less than? a. 5.59 b. 4.52 c. 2 d. 8 11. Which of the following measurements is resistant (is not be greatly affected by an outlier)? a. Mean b. Standard Deviation c. Range d. Median 12. Calculate the interquartile range for the data. (Do not round your answer). 13. Based on a comparison of the mean and the median, what is the shape of the distribution? a. Left Skewed b. Right Skewed c. Symmetric 14. Using the number line provided, draw the boxplot. 15. State one categorical variable that could be collected for this sample (any variable is fine, it just has to be categorical). a. Left skewed b. Right skewed c. Symmetric

16. State one graph you could use to display a categorical variable (only list one, if you list multiple and one is incorrect the entire problem will be marked incorrect). Use the following information to answer questions 17 to 21: Assume the distribution company has trucks that deliver the same item; therefore, the number of boxes that can fit in the truck and the weight of the boxes follow a symmetric, bell-shaped (normal) distribution. (This does assume the same number of boxes are on each truck.) Assume the mean weight of the trucks loaded with boxes is known to be 45,000 pounds with a standard deviation of 1,000 pounds. 17. State briefly, why we know the empirical rule can be used for this situation. (One sentence.) 18. What percentage of the trucks loaded with boxes weigh between 43,000 pounds and 47,000 pounds? 19. Calculate the z-score for a truck loaded with boxes that weighs 41,880 pounds. (Round your answer to 2 decimal places). 20. Interpret the z-score you calculated in the previous question (for a truck loaded with boxes that weighs 41,880 pounds). 21. Would a truck loaded with boxes that weighs 41,880 pounds be an unusual value? Justify your answer using the z-score calculated. (No justification, no credit).

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Use the following to answer questions 22 - 24: Assume a distribution company has only three loading docks for trucks (A, B, and C). Each time a truck is loaded there is a record made as to whether the truck left on time or late from the loading dock (note if a truck left ahead of schedule it is classified as on time). The following tree diagram shows the results of a study of trucks based on loading dock used and whether the truck left on time. OT A OT C OT B OT C OT C OT C 22. Based on the tree diagram, what is the probability that a truck leaves from loading dock C? a. 0.15 b. 0.25 c. 0.80 d. 1.00 23. Based on the tree diagram, what is the probability that a truck is on time given it leaves from loading dock B? a. 0.23 b. 0.35 c. 0.27 d. 0.77 24. Based on the tree diagram, what is the probability that a truck leaves from loading dock A and is on time? a. 0.40 b. 0.10 c. 0.4 x 0.75 = 0.30 d. 0.75 0.75 Notation used in tree diagram: A = Truck left from loading dock A B = Truck left from loading dock B C = Truck left from loading dock C OT = Truck left on time (or ahead of schedule) OT C = Truck left late. (Not on time) 0.40 0.77 0.35 0.80

Use the following to answer questions 25 - 30: The workers at a distribution center that load the trucks quickly inspect the boxes before they put them on the truck to determine if they appear to be damaged. If a package is damage it is replaced by a not damaged package. The following table shows the result of a random sample of 100 packages with the size of the package and whether or not it was damaged. Use the contingency table given to answer the questions that follow: Small Package (less than 5 pounds) Medium Package (between 5 pounds and 20 pounds) Large Package (over 20 pounds) Total Damaged 2 3 5 10 Not Damaged 30 35 25 90 Total 32 38 30 100 25. What is the probability that a randomly selected package is damaged? (Round to 2 decimal places) 26. What is the probability that a randomly selected package is medium in size? (Round to 2 decimal places) 27. What is the probability that a randomly selected package is damaged and medium in size? (Round to 2 decimal places) 28. What is the probability that a randomly selected package is damaged or medium in size? (Round to 2 decimal places) 29. What is the probability that a randomly selected package is damaged given it is medium in size? (Round to 2 decimal places)

30. Are the event damaged package and medium in size independent? Justify your answer using probabilities.

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