PracticeExamV2

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350

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Statistics

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Apr 3, 2024

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ST350 Exam 1 Practice Exam Page 1 of 10 NOTE to students: 1. This is intended to give you an idea of the type questions the instructor asks and the approximate length of the exam. It does NOT indicate the exact questions or the topics covered. Students should refer to the learning objectives in the appropriate study guides to determine the coverage of the material. 2. Please read the for details about what are allowed and what are not allowed in the exam as well as the sanctions. Solutions are listed at the end of this document. Instructions: • Read each question carefully • Choose or enter the best answer. There is no need to explain. • If you need to calculate a number, please try not to round during intermediate step, if you have to, round to at least 4 decimals. Round to 4 decimals for your final answer if not otherwise specified

ST350 Exam 1 Practice Exam Page 2 of 10 Each multiple choice question is worth 3 points, no partial credit. 1. Which of the following variables is Nominal? a. Age (in years) b. Age (grouped as: less than 18, 18-29, 30-59, 60 and older) c. Car color (e.g. red, blue, grey) d. Letter grade in a course (e.g. A+, A, A-, B+, B) 2. Which of the following graphical summaries is most appropriate for a numeric variable? a. Bar chart b. Histogram c. Boxplot d. Both b. and c. but not a. 3. An administrator for a large community college knows that 82% of the students at the school receive financial aid. The administrator is going to take a sample of 100 students to complete a survey about the costs of attending that college. Which formula would be used to calculate the standard deviation of the sample proportion in this situation? a. 0 . 82 100 b. 0 . 82 √100 c. ( 0 . 82 )( 0 . 18 ) 100 d. � ( 0 . 82 )( 0 . 18 ) 100 4. A researcher for a clothing company has found that the shoulder to wrist length for adult females is normally distributed with a mean of 19 inches and a standard deviation of 2 inches. Which picture represents the probability that a randomly selected female has a shoulder to wrist length over 20 inches?

ST350 Exam 1 Practice Exam Page 3 of 10 a. b. c. d. 5. Consider the distribution of shoulder to wrist length from the previous question. Which picture represents the first quartile of this distribution? (Note: in each picture, the shaded area represents a probability of 0.25.) d. c. b. a.

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ST350 Exam 1 Practice Exam Page 4 of 10 Use the data visualization at the right to answer questions 6 and 7 . 6. This type of visualization is best suited for a. Summarizing a categorical variable b. Summarizing a quantitative variable c. Summarizing a numeric variable d. Both b. and c. but not a. 7. Does this visualization accurately display the story of the data? a. Yes, a bar chart is the best display for this data. b. No, a pie chart would be a better display for this data. c. Yes, Happajoy is more effective at reducing allergy symptoms than Pollaway. d. No, the difference in effectiveness between Happajoy and Pollaway has been exaggerated. Use the following for questions 8 and 9. An insurance company offers policies for cars that are considered for “casual use”. Owners of these cars pay a lower premium rate but are limited to driving them less than 8,000 miles a year. An executive with the company wants to determine the average number of miles cars with these policies were driven last year. She pulls a list of all the cars with these policies at the company and randomly selects 100 of them. She then contacts each of the drivers of these and asks them to report the number of miles driven last year. The survey found the average number of miles driven was 4330. 8. What is the sampling frame in this situation? a. The list of all cars with this type of policy from his company. b. All vehicles the company insures with casual use policies. c. The 100 cars that were randomly selected. d. All vehicles in the U.S. with casual use policies. 9. Which of the following would be an example of undercoverage in this study? a. If the car owners lied about the amount of miles driven because they did not want to pay the additional premium for being over 8000 miles. b. If the list of cars only includes cars from households that have two vehicles. c. If some of car owners refused to report the number of miles they had driven. d. Both b. and c. but not a. 10. The Normal distribution a. is always bi-modal.

ST350 Exam 1 Practice Exam Page 5 of 10 b. is always symmetric. c. is always skewed to the left. d. is always skewed to the right. 11. A high school teacher gave her students an in-class quiz worth 25 points. The class average was only 12 points, so she decided to curve the scores by adding 5 points to each. What can we conclude about the mean of the curved scores? a. It must be equal to 12. b. It must be equal to 17. c. It must be equal to the median of the curved scores. d. It is impossible to tell what the mean of the curved scores will be. 12. We should be wary of a poll that has a high non-response rate because a. those who refused to respond may be different from those who participate. b. the sampling frame must not have been representative of the population. c. the standard deviation will be very large. d. the mean and median will be different because the results are skewed. 13. An experiment is said to be double-blind if a. there is no control group. b. the subjects do not know which treatment they are receiving. c. the experimenter does not know which treatment the subjects are receiving. d. Both b. and c. but not a.

ST350 Exam 1 Practice Exam Page 6 of 10 Use the following for questions 14 to 15. A survey of 319 undergraduate students asked for the amount they had spent on lunch the previous day. The resulting data was used to produce this histogram. 14. The shape of this distribution would be best described as: a. Clearly symmetric b. Slightly skewed to the right c. Slightly skewed to the left d. Clearly bi-modal 15. There is an outlier at $25 in this data set. If it were changed to $21 which of the following would change? a. The median. b. The mean. c. The minimum. d. Both a. and b. but not c. 16. The median of the data set (including the outlier) is most likely… a. $25 b. $15 c. $7 d. $3 17. An educational software company places a “quick vote” poll on a website, asking users to indicate whether they like or dislike the software. Of 900 respondents, 610 said they liked the software. The results of the sample are probably a. unbiased, because of the large sample size. b. biased, because it is a voluntary response sample. c. unbiased, because it is a simple random sample. d. biased, because a larger sample should be used.

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ST350 Exam 1 Practice Exam Page 7 of 10 Use the following for questions 18 and 19. An administrator for a school district in the Midwest is comparing two grade schools on their end of grade tests for 5th graders. The administrator made the following boxplots of the data 18. From these boxplots we see that the shape of the histogram of school 2 would be a. more skewed to the right than school 1. b. more skewed to the left than school 1. c. clearly bimodal. d. more symmetric than school 1. 19. From the boxplots we see a. the students at both schools have very similar test scores. b. students' test scores have similar medians but school 1 has a much higher standard deviation. c. students at school 1 generally scored much higher than students at school 2. d. students at school1 generally scored much lower than school 2. 20. A case contains 20 burglar alarms. If the probability of selecting a defective alarm from this case is 0.01 and the trials are independent, how would you calculate the probability that at least one of the alarms is defective? a. Calculate P (1 success) using the Binomial distribution b. Calculate 1- P (1 success) using the Binomial distribution c. Calculate 1- P (0 success) using the Binomial distribution d. Calculate the standard score and use the normal distribution

ST350 Exam 1 Practice Exam Page 8 of 10 21. You calculate the standard deviation of a data set and find that it is –1.23. From this you can determine that a. every value in the data set is the same. b. you made an arithmetic mistake. c. the mean must be negative d. all values in the data set are negative. Use the following for questions 22 to 24: Does "listening" to classical music make plants grow? 40 potted house plants were randomized to be either in a room while classical music was played from a radio or in a room with no music, with 20 plants being randomly assigned to each type of room. The rooms had similar amounts of light and the plants were given the same amount of water during the study. The size of the plants was measured at the start of the study and again after two weeks, and the amount of growth for each plant was calculated. It was found that the plants in the room where classical music was played were significantly larger, on average, than the plants in the room with no music. 22. This study is best described as a. an observational study. b. a matched pairs design. c. a randomized block design. d. a completely randomized design. 23. In this study, the response variable was a. the 40 potted house plants. b. the rooms with and without classical music. c. the size of the plant at the end of the study d. the amount of growth for each plant. 24. In this study, the primary purpose of random assignment is a. to ensure that the experimenter doesn't know whether a plant was in the room with or without classical music. b. to ensure that the groups are similar in all respects except for whether or not classical music was played in the room. c. to ensure that the study participants are representative of the population. d. to account for the placebo effect. 25. Suppose that, for random samples of n = 100, the sampling distribution of 𝑥𝑥𝑥𝑥 𝑥 is normal with mean 60 and standard deviation 13. Which of the following provides the best interpretation of this standard deviation? a. We expect the possible values of the sample proportion to be about 13% away from the true population proportion of 60%. b. We expect the possible values of the sample mean to be about 13 points away from the true population mean of 60. c. We expect the possible values of the sample proportion to be about 60% away from the true population proportion of 13%. d. We expect the possible values of the sample mean to be about 60 points away from the true population mean of 13.

ST350 Exam 1 Practice Exam Page 9 of 10 Use the following for questions 26 to 28. A researcher is interested in estimating the percentage of North Carolina State University students that have an Amazon Prime account. The researcher believes that this percentage is related to the age of the students. The researcher gets a list of all students at the university and separates the list into two groups. One group contains students younger than 21 and the other group contains students 21 or older. The researcher takes a random sample from both groups, contacts each person that was selected in the sample and calculates the percentage in each group that have an Amazon Prime account. 26. In this situation what is the population of interest? a. The list of all students at North Carolina State University. b. All students at North Carolina State University. c. All students at North Carolina State University with an Amazon Prime account. d. The proportion of all students at North Carolina State University that have an Amazon Prime account. 27. In this situation what is the parameter of interest? a. The proportion of all students at North Carolina State University that have an Amazon Prime account. b. All students at North Carolina State University c. All students at North Carolina State University with an Amazon Prime account. d. The list of all students at North Carolina State University. 28. In this situation the sample is best described as a. a volunteer response sample. b. a stratified random sample with age groups as strata. c. a cluster random sample with age groups as clusters. d. a simple random sample. 29. The most important advantage of experiments over observational studies is that a. experiments are usually easier to carry out. b. experiments can give better evidence of causation. c. the placebo effect cannot happen in experiments. d. an observational study cannot have a response variable. 30. True or False: A heat map is useful representing a variable that has a spatial element to it. a. True b. False 31. Sampling variability a. is the variation in sample statistics that results from error in the process of selecting different samples. b. is the variation in sample statistics that results from selecting different random samples. c. has a predictable pattern that makes statistical inference possible. d. Both b. and c. but not a.

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ST350 Exam 1 Practice Exam Page 10 of 10 32. The standard error of a statistic describes a. the variability of a sample statistic. b. the variability of the individuals. c. the error that occurs due to non-response and measurement errors. d. all of the above. 33. True False A standard score is always between –1 and +1.

ST350 Exam 1 Practice Exam Page 10 of 10 Solutions 1. C 2. D 3. D 4. A 5. B 6. A 7. D 8. A 9. B 10. B 11. B 12. A 13. D 14. B 15. B 16. C 17. B 18. A 19. C 20. C 21. B 22. D 23. D 24. B 25. B 26. B 27. A 28. B 29. B 30. A 31. D 32. A 33. False

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