Statistics Question

Mathematics

STATISTIC

univesity of queensland

Question Description

Statistic Exam 29/1/2021 9.15am - 12.25 pm Melbourne time

Check the conclusion file thats the exam structure, attacted 2 sample notes as well. Will send the student access for studying. after hire.

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1 TSTA602 Workshop 3 Problem Set 1. Consider an investment of $100,000 that declined to a value of $50,000 at the end of the first year and recovered back to $100,000 at the end of the second year. Calculate the arithmetic mean and the geometric mean of the annual rates of return of this investment, and comment on your results. 2. Two populations, A and B, have the same coefficient of variation. If A’s mean is four times as large as B’s, then A’s standard deviation is: a. twice as large as B’s c. four times as large as B’s b. half as large as B’s d. unknown from the given information 3. There are 7 members of the crew of a space shuttle. On earth they weigh 98, 77, 63, 101, 85, 49 and 94 kilograms. Find the mean, median, population standard deviation and range of the weights on Earth. 2 4. The following information shows the calories and fat in 500ml (approx.) drinks available from a number of outlets: a. For each variable, compute the mean, median, mode, first quartile and third quartile. b. For each variable, compute the sample variance, sample standard deviation, range, interquartile range, coefficient of variation. Are the data skewed? If so, how? 3 5. A bank branch located in a commercial district of a city has developed an improved process for serving customers during the noon-1pm lunch period. The waiting time, in minutes of a sample of 15 customers during this hour is recorded over a week. The results are: a. Calculate the mean, median, first quartile and third quartile b. Calculate the variance, sample standard deviation, range, interquartile range, coefficient of variation. c. Are the data skewed? If so, how? d. A customer walks into the branch during the lunch hour and asks the branch manager how long a wait she can expect. The branch manager replies, “Almost certainly less than five minutes.” On the basis of your results to parts a. –c., comment on the manager’s rely. 6. A population of TSTA602 students is known to have a mean final mark of 65 and a standard deviation of 5. The population is known to be bell-shaped. Describe the distribution of final marks. Is it likely that a student will fail this unit? Is it likely that a student will achieve above 80? 7. a. Calculate the 5-number summary for the following data: 5 4 7 13 20 9 12 21 23 19 17 b. Discuss the skewness of the data. 4 8. An owner of a restaurant is interested in examining the demand for dessert over a given time period. She is worried that the size of entrées is too large, therefore affecting whether or not patrons order dessert. If this is the case, it would have an impact on her profit. She collects data on whether a dessert is ordered and whether an entrée is ordered for a sample of 1000 patrons. She finds the following: a. Among the patrons who do not order dessert, what is the percentage of those having ordered entrée? Can the owner make a decision on the size of the entrée based on this percentage? Explain. b. Produce a side-by-side bar chart and a stacked bar chart based on this contingent table using MS Excel. Comment on these two charts. Discuss again whether the owner should reduce the size of the entrée. 9. Use the calories and fat data in question 4 (see data in WS3.xlsx), compute a. The sample covariance b. The coefficient of correlation Which do you think is more informative in expressing the relationship between calories and fat? Explain. What conclusion do you reach about the relationship between calories and fat? Produce a scatter plot using MS Excel and comment on the result. 1 TSTA602 Workshop 8 Problem Set 1. The following data represent the number of days absent per year in a population of six employees of a small company: 1 3 6 7 9 10. Assuming that you randomly select a sample of n=2 with replacement and construct the sampling distribution of the mean. Compute the mean of all the sample means and also compute the population mean. Are the equal? What is this property called? 2. The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes. A random sample of 16 cars is selected. a. What is the probability that a sample mean is between 45 and 52 minutes? b. What is the probability that the sample mean is between 39 and 48 minutes? 3. An automatic machine filling soup cans has μ = 500ml and σ = 20ml. A sample of 64 cans is inspected. a. What is the probability that a sample mean fill is greater than 504.5ml? b. What is the probability that a sample mean fill is less than 499.5ml? 4. A sample of 364 employees’ hourly wages was observed. The mean wage of all employees in the firm is $17.50 per hour with a standard deviation of $5.20. The observed sample mean will lie within which two values, symmetric about the mean with a 92% probability? 5. The quality control manager at a light bulb factory needs to estimate the mean life of a large shipment of light bulbs. The standard deviation is 100 hours. A random sample of 64 light bulbs indicated a sample mean life of 350 hours. a. Construct a 95% confidence interval estimate of the population mean life of light bulbs in this shipment and interpret your result. b. Do you think that the manufacturer has the right to state that the light bulbs last an average of 400 hours? Explain. c. Must you assume that the population of light bulb life is normally distributed? Explain. Registered Higher Education Provider TEQSA PRV12059 | CRICOS Code: 02491D Top Education Group Ltd ACN 098 139 176 trading as Australian National Institute of Management and Commerce (IMC) TSTA602 Quantitative Methods for Accounting and Finance Modern Business Statistics, 7e Anderson, Sweeney, Williams, Camm, Cochran, Fry, Ohlmann © 2021 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Contact Details • Lecturer: Dr Biplob Chowdhury • Email: biplob.chowdhury@imc.edu.au • Consultation: by email and appointment only 3 | Australian National Institute of Management and Commerce (IMC) Chapter 1: Data and Statistics          Statistics Applications in Business and Economics Data Sources Descriptive Statistics Statistical Inference Statistical Analysis Using Microsoft Excel Analytics Big Data and Data Mining Ethical Guidelines for Statistical Practice 4 | Australian National Institute of Management and Commerce (IMC) Chapter 2, Part A Descriptive Statistics: Tabular and Graphical Displays  Summarizing Data for a Categorical Variable  Categorical data use labels or names to identify categories of like items.  Summarizing Data for a Quantitative Variable  Quantitative data are numerical values that indicate how much or how many. 5 | Australian National Institute of Management and Commerce (IMC) Chapter 2, Part B Descriptive Statistics: Tabular and Graphical Displays  Summarizing Data for Two Variables Using Tables  Summarizing Data for Two Variables Using Graphical Displays  Data Visualization: Best Practices in Creating Effective Graphical Displays 6 | Australian National Institute of Management and Commerce (IMC) Chapter 3, Part A Descriptive Statistics: Numerical Measures  Measures of Location  Measures of Variability 7 | Australian National Institute of Management and Commerce (IMC) Chapter 3, Part B Descriptive Statistics: Numerical Measures  Measures of Distribution Shape, Relative Location, and Detecting Outliers.  Five-Number Summaries and Boxplots  Measures of Association Between Two Variables  Data Dashboards: Adding Numerical Measures to Improve Effectiveness 8 | Australian National Institute of Management and Commerce (IMC) Chapter 4 Introduction to Probability  Experiments, Counting Rules, and Assigning Probabilities  Events and Their Probabilities  Some Basic Relationships of Probability  Conditional Probability  Bayes’ Theorem 9 | Australian National Institute of Management and Commerce (IMC) Chapter 5 Discrete Probability Distributions        Random Variables Developing Discrete Probability Distributions Expected Value and Variance Bivariate distributions and Covariance Financial Portfolios Binomial Probability Distribution Poisson Probability Distribution 10 | Australian National Institute of Management and Commerce (IMC) Chapter 6 Continuous Probability Distributions • Uniform Probability Distribution • Normal Probability Distribution • Exponential Probability Distribution 11 | Australian National Institute of Management and Commerce (IMC) Chapter 7 Sampling and Sampling Distributions  Selecting a Sample  Point Estimation  Introduction to Sampling Distributions  Sampling Distribution of x • Sampling Distribution of p • Other Sampling Methods • Big data and Errors in Sampling 12 | Australian National Institute of Management and Commerce (IMC) Chapter 8 Interval Estimation      Population Mean: σ Known Population Mean: σ Unknown Determining the Sample Size Population Proportion Big data and Interval estimation 13 | Australian National Institute of Management and Commerce (IMC) Chapter 9 Hypothesis Testing  Developing Null and Alternative Hypotheses  Type I and Type II Errors  Population Mean: σ Known  Population Mean: σ Unknown  Population Proportion 14 | Australian National Institute of Management and Commerce (IMC) Chapter 14, Part A Simple Linear Regression  Simple Linear Regression Model  Least Squares Method  Coefficient of Determination  Model Assumptions  Testing for Significance 15 | Australian National Institute of Management and Commerce (IMC) Chapter 14, Part B Simple Linear Regression  Using the Estimated Regression Equation for Estimation and Prediction  Excel’s Regression Tool  Residual Analysis: Validating Model Assumptions  Outliers and Influential Observations 16 | Australian National Institute of Management and Commerce (IMC) Chapter 15 Multiple Regression         Multiple Regression Model Least Squares Method Multiple Coefficient of Determination Model Assumptions Testing for Significance Using the Estimated Regression Equation for Estimation and Prediction Categorical Independent Variables Residual Analysis 17 | Australian National Institute of Management and Commerce (IMC) How will I be Assessed 18 | Australian National Institute of Management and Commerce (IMC) Requirements to Pass the Unit Requirements to Pass the Unit  To achieve a passing grade in this unit a student must: (a)Attempt all within-term assessment tasks to the satisfaction of the lecturerin-charge; (b)Attend the final examination and submit a completed examination script; and (c)Achieve an overall mark of at least 50% in the unit. 19 | Australian National Institute of Management and Commerce (IMC) Final Exam Instructions: Answer all THREE (3) Questions. Please type your answers immediately following each question. Be sure to read all instructions and questions carefully before answering. Make use of formulae and graphs to clarify your answers, as and when possible. Show all steps when calculations are involved. Section Question format Number of questions Worth Each Question comprises of multiple parts. Answer all THREE (3) questions. 100 marks Total 100 marks Time Management: Time Allowed: 3 hours – 180 minutes Total marks: 100 marks The examination counts for 40 percent of the marks for this unit. But!!Read Chapter Carefully Week 1 2 3 4 5 6 7 8 9 10 11 Topic/s and activities Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 14 Chapter 15 What To Study For The Final Exam? • Workshop questions • Lecture material • Assignment • Please do not study previous exam papers 3-hour Final Exam 23 | Australian National Institute of Management and Commerce (IMC) 24 | Australian National Institute of Management and Commerce (IMC) ...
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