Mathematics
University of Southern California Finding the Statistical Values Exam Practice

MCJ 5100

University of Southern California

MCJ

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MCJ5100 Advance Research Methods and Analysis I Final Exam Review: Winter Quarter 2020 Identify the population and sample in the following study. 1. A study of dietary habits of 20,000 men was conducted to find link between high intakes of dairy products and prostate cancer. Determine whether the numerical value is a parameter or a statistic. 2. In a survey of 2253 Internet users, 19% use Twitter or another service to share social updates. 3. At college 90% of the Board of Trustees members approved the contract of the new president. Determine whether the data are qualitative or quantitative. 4. A list of debit card pin numbers. 5. The final scores on a video game. Identify each data’s level of measurement (nominal, ordinal, interval, ratio) 6. A list of badge numbers of police officers at a precinct. 7. The horespowers of racing car engines. 8. The top 10 grossing films released in 2019. 1 9. The years of birth for the numbers in the Boston marathon. Determine which method of data collection (observation, experiment, stimulation, survey) you would use to gather data for each study. 10. A study on the effect of low dietary intake of vitamin C and iron on lead levels in adults. 11. The ages of people living within 500 miles of your home. Identify the sampling technique used in each study. 12. A journalist goes to a campground to ask people how they feel about air pollution. 13. For quality assurance, every tenth machine part is selected from an assembly line and measured for accuracy. 14. A study of attitudes about smoking is conducted at a college. The students are divided by class (freshman, sophomore, junior, and senior). Then a random sample is selected from each class and interviewed. 15. The data set represents the number of minutes a sample of 25 people exercise each week. 108 157 127 139 150 128 120 124 139 123 111 119 120 101 118 132 135 114 123 119 127 131 116 131 117 a. Make a frequency distribution of the data set using five classes. Include class limits, midpoints, boundaries, frequencies, relative frequencies, cumulative frequency, and class boundaries. 2 Class Frequency (f) Midpoint Relative Frequency Cumulative Frequency Class Boundaries b. Display the data using a frequency histogram. c. Describe the distribution’s shape as symmetric, uniform, or skewed. d. Display the data using a stem-and-leaf plot. Use the first two numbers of each number (For example 115, use “11”) e. Use the frequency distribution formulas to find the sample mean and the sample standard deviation of the data set. 3 16. Weekly salaries salaries (in dollars) for a sample of registered nurses are listed. 774 446 1019 795 908 667 444 960 a. Find the mean, median, mode of the salaries. i. Mean = ii. Median = iii. Mode = b. Find the range, variance, and standard deviation of the data set. i. Range = ii. Variance = iii. Standard Deviation = c. Interpret the results in the context of the real-life setting. 17. The mean price of new homes from a sample of houses is $155,000 with a standard deviation of $15,000. The data set has a bell-shaped distribution. Use the z-scores to determine which, if any, of the following house prices is unusual. a. $200,000 i. Z= b. $55,000 i. Z= 18. The number of regular season wins for each Major League Baseball team in 2009 are listed. a. Find the five-number summary of the data set. i. Min = ii. Q1 = iii. Q2 = iv. Q3 = v. Max = b. Find the interquartile range. i. c. Display the data using a box-and-whisker-plot. 19. Identify the sample space of the probability experiment and determine the number of outcomes in the event. Draw a tree diagram if it is appropriate. 4 a. Experiment: Tossing four coins. b. Event: Getting three heads. i. Sample space: 20. Use the fundamental counting principle: A student must choose from 7 classes to take at 8:00 a.m., 4 classes to take at 9:00 a.m., and 3 classes to take at 10:00 a.m. How many ways can the student arrange the schedule? 21. Classify the statement as an example of classical probability, empirical probability, or subjective probability. a. On the basis of prior counts, a quality control says there is a 0.05 probability that a randomly chosen part is defective. b. The probability of randomly selecting five cards of the same suit from a standard deck is about 0.0005. c. The chance that Corporation A’s stock price will fall today is 75%. 5 22. The table below shows the number (in thousands) of earned degrees, by level and gender, conferred in the United States in a recent year. Level of Degree Gender Male Gender Female Total Associate’s 275 453 728 Bachelor’s 650 875 1525 Master’s 238 366 604 Doctoral 30 30 60 Total 1193 1724 2917 A person who earned a degree in the year is randomly selected. Find the probability of selecting someone who: a. Earned a bachelor’s degree given that the person is a female. b. Earned an associate’s degree or a bachelor’s degree. c. Earned a doctorate given that the person is a male. 23. Decide if the events are mutually exclusive. Then decide if the events are independent or dependent. a. Event A: A golfer scoring the best round in a four-round tournament. b. Event B: Losing the golf tournament. 24. The access code for a warehouse’s security system consists of six digits. The first digit cannot be 0 and the last digit must be even. How many different codes are available? 25. From a pool of 30 candidates, the offices of president, vice president, secretary, and treasurer will be filled. In how many ways can the offices be filled? 6 26. 11P2 27. 5C3/10C3 28. A card is randomly selected from a standard deck. Find the probability that the card is red or a queen. 29. A 12-sided die, number 1 to 12, is rolled. Find the probability that the roll results in an odd number of a number less than 4. 30. Five players on a basketball must each choose a player on the opposing team to defend. In many ways can they choose their defensive assignments? 31. Decide whether the random variable x is discrete or continuous. a. Let x represent the amount of carbon dioxide emitted from a car’s tailpipe each day. b. Let x represent the number of people that activate a metal detector at an airport each hour. 32. Decide whether the distribution is a probability distribution. If it is not, identify the property that is not satisfied. x 1 2 3 4 5 6 7 8 P(x) 1/80 2/75 1/10 12/25 27/30 1/5 2/25 1/120 7 33. Determine the probability distribution that is missing. x 0 1 2 3 4 P(x) 0.07 0.20 .38 ? 0.13 34. The number of televisions per household in a small town. Television 0 1 2 3 Households 26 442 728 1404 Use the probability distribution or histogram to find the: a. b. c. d. Mean Variance Standard deviation Expected value 35. To left of z = 0.33 36. To The right of z = 3.22 37. Between z = -1.55 and z = 1.04 38. Determine whether the hypothesis test with the given null and alternative hypothesis is left-tailed, right tailed, or two tailed. a. Ho:p=0.25 Ha:p​≠0.25 39. Determine whether the hypothesis test with the given null and alternative hypothesis is left-tailed, right tailed, or two tailed. a. Ho:​μ≤8.0 Ha:μ>8.0 40. Write the claim as a mathematical sentence. a. A light bulb manufacturer claims that the mean life of a certain light bulb is more than 750 hours. 8 b. A stated by a company’s shipping department, the number of shipping errors per million shipments has a standard deviation that is less than 3. c. The standard deviation of the base price of a certain type of all-terrain vehicle is no more than $320. 9 MCJ5100 Advance Research Methods and Analysis I Final Exam Review: Winter Quarter 2020 Identify the population and sample in the following study. 1. A study of dietary habits of 20,000 men was conducted to find link between high intakes of dairy products and prostate cancer. Determine whether the numerical value is a parameter or a statistic. 2. In a survey of 2253 Internet users, 19% use Twitter or another service to share social updates. 3. At college 90% of the Board of Trustees members approved the contract of the new president. Determine whether the data are qualitative or quantitative. 4. A list of debit card pin numbers. 5. The final scores on a video game. Identify each data’s level of measurement (nominal, ordinal, interval, ratio) 6. A list of badge numbers of police officers at a precinct. 7. The horespowers of racing car engines. 8. The top 10 grossing films released in 2019. 1 9. The years of birth for the numbers in the Boston marathon. Determine which method of data collection (observation, experiment, stimulation, survey) you would use to gather data for each study. 10. A study on the effect of low dietary intake of vitamin C and iron on lead levels in adults. 11. The ages of people living within 500 miles of your home. Identify the sampling technique used in each study. 12. A journalist goes to a campground to ask people how they feel about air pollution. 13. For quality assurance, every tenth machine part is selected from an assembly line and measured for accuracy. 14. A study of attitudes about smoking is conducted at a college. The students are divided by class (freshman, sophomore, junior, and senior). Then a random sample is selected from each class and interviewed. 15. The data set represents the number of minutes a sample of 25 people exercise each week. 108 157 127 139 150 128 120 124 139 123 111 119 120 101 118 132 135 114 123 119 127 131 116 131 117 a. Make a frequency distribution of the data set using five classes. Include class limits, midpoints, boundaries, frequencies, relative frequencies, cumulative frequency, and class boundaries. 2 Class Frequency (f) Midpoint Relative Frequency Cumulative Frequency Class Boundaries b. Display the data using a frequency histogram. c. Describe the distribution’s shape as symmetric, uniform, or skewed. d. Display the data using a stem-and-leaf plot. Use the first two numbers of each number (For example 115, use “11”) e. Use the frequency distribution formulas to find the sample mean and the sample standard deviation of the data set. 3 16. Weekly salaries salaries (in dollars) for a sample of registered nurses are listed. 774 446 1019 795 908 667 444 960 a. Find the mean, median, mode of the salaries. i. Mean = ii. Median = iii. Mode = b. Find the range, variance, and standard deviation of the data set. i. Range = ii. Variance = iii. Standard Deviation = c. Interpret the results in the context of the real-life setting. 17. The mean price of new homes from a sample of houses is $155,000 with a standard deviation of $15,000. The data set has a bell-shaped distribution. Use the z-scores to determine which, if any, of the following house prices is unusual. a. $200,000 i. Z= b. $55,000 i. Z= 18. The number of regular season wins for each Major League Baseball team in 2009 are listed. a. Find the five-number summary of the data set. i. Min = ii. Q1 = iii. Q2 = iv. Q3 = v. Max = b. Find the interquartile range. i. c. Display the data using a box-and-whisker-plot. 19. Identify the sample space of the probability experiment and determine the number of outcomes in the event. Draw a tree diagram if it is appropriate. 4 a. Experiment: Tossing four coins. b. Event: Getting three heads. i. Sample space: 20. Use the fundamental counting principle: A student must choose from 7 classes to take at 8:00 a.m., 4 classes to take at 9:00 a.m., and 3 classes to take at 10:00 a.m. How many ways can the student arrange the schedule? 21. Classify the statement as an example of classical probability, empirical probability, or subjective probability. a. On the basis of prior counts, a quality control says there is a 0.05 probability that a randomly chosen part is defective. b. The probability of randomly selecting five cards of the same suit from a standard deck is about 0.0005. c. The chance that Corporation A’s stock price will fall today is 75%. 5 22. The table below shows the number (in thousands) of earned degrees, by level and gender, conferred in the United States in a recent year. Level of Degree Gender Male Gender Female Total Associate’s 275 453 728 Bachelor’s 650 875 1525 Master’s 238 366 604 Doctoral 30 30 60 Total 1193 1724 2917 A person who earned a degree in the year is randomly selected. Find the probability of selecting someone who: a. Earned a bachelor’s degree given that the person is a female. b. Earned an associate’s degree or a bachelor’s degree. c. Earned a doctorate given that the person is a male. 23. Decide if the events are mutually exclusive. Then decide if the events are independent or dependent. a. Event A: A golfer scoring the best round in a four-round tournament. b. Event B: Losing the golf tournament. 24. The access code for a warehouse’s security system consists of six digits. The first digit cannot be 0 and the last digit must be even. How many different codes are available? 25. From a pool of 30 candidates, the offices of president, vice president, secretary, and treasurer will be filled. In how many ways can the offices be filled? 6 26. 11P2 27. 5C3/10C3 28. A card is randomly selected from a standard deck. Find the probability that the card is red or a queen. 29. A 12-sided die, number 1 to 12, is rolled. Find the probability that the roll results in an odd number of a number less than 4. 30. Five players on a basketball must each choose a player on the opposing team to defend. In many ways can they choose their defensive assignments? 31. Decide whether the random variable x is discrete or continuous. a. Let x represent the amount of carbon dioxide emitted from a car’s tailpipe each day. b. Let x represent the number of people that activate a metal detector at an airport each hour. 32. Decide whether the distribution is a probability distribution. If it is not, identify the property that is not satisfied. x 1 2 3 4 5 6 7 8 P(x) 1/80 2/75 1/10 12/25 27/30 1/5 2/25 1/120 7 33. Determine the probability distribution that is missing. x 0 1 2 3 4 P(x) 0.07 0.20 .38 ? 0.13 34. The number of televisions per household in a small town. Television 0 1 2 3 Households 26 442 728 1404 Use the probability distribution or histogram to find the: a. b. c. d. Mean Variance Standard deviation Expected value 35. To left of z = 0.33 36. To The right of z = 3.22 37. Between z = -1.55 and z = 1.04 38. Determine whether the hypothesis test with the given null and alternative hypothesis is left-tailed, right tailed, or two tailed. a. Ho:p=0.25 Ha:p​≠0.25 39. Determine whether the hypothesis test with the given null and alternative hypothesis is left-tailed, right tailed, or two tailed. a. Ho:​μ≤8.0 Ha:μ>8.0 40. Write the claim as a mathematical sentence. a. A light bulb manufacturer claims that the mean life of a certain light bulb is more than 750 hours. 8 b. A stated by a company’s shipping department, the number of shipping errors per million shipments has a standard deviation that is less than 3. c. The standard deviation of the base price of a certain type of all-terrain vehicle is no more than $320. 9 ...
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