Assignment 4 - Part 2

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University of Ottawa *

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2303

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Statistics

Date

Jan 9, 2024

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Assignment 4 - Part 2 ADM2303, Fall 2023 • The assignment is due on Sunday, Dec 3 at 11:59 pm • The total point for this assignment is 37 points. • For information regarding penalties, refer to the course outline "Part 2 Marking Scheme" • The solution file must be type-written and submitted on Brightspace in PDF format • You can use Microsoft Excel to carry out your calculations. However, you must show the detailed step by step calculations and process in your solution file. • Include a statement of academic integrity in your submission. • You are responsible for completing this assignment on your own. The integrity statement prohibits receiving assistance in answering questions through any form of service. Question #1: [10 marks] Quantitative Data The following data represents alcohol consummation (g/week) from the respondents, including beer bottles, wine bottles and spirits (strong alcoholic drinks). We would like to obtain, for this 116 respondents’ dataset the following information. (NB: the dataset is available in the Excel file provided in Brightspace folder “Assignment 4 – Part 2”.) NOTE: YOU CANNOT USE ANY STATISTICAL FUNCTIONS TO ANSWER THE QUESTIONS BELOW. YOU MUST USE THE APPROACHES TAUGHT IN WEEK 9 MATERIAL AND IN CHAPTER 5 OF YOUR TEXTBOOK. YOU MUST SHOW THE STEPS THAT YOU TOOK TO GET YOUR ANSWER. a) Identify the variable for this study. b) Find the mode. c) Find the five-number summary. d) Find the interquartile range. e) Find the 55 th percentile. f) Find the coefficient of variation (CV) given that the variance is equal to 2098.270. g) Provide a histogram using an interval of 30 starting with a lower bound of 10 not inclusive. For example: more than 10 and equal to 20, more than 20 and equal to 30, etc. h) Using the histogram obtained in g), find the mean for this histogram, and compare with the mean found in f). Question #2: [5 marks] Surveys and Sampling - Canadian Labour Force Survey Most people have heard of the unemployment rate, but not so many know where it comes from. Does the rate simply represent the number of people claiming Employment Insurance (EI)? It turns out that would be an underestimation of the number of people unemployed, since many people are unemployed but ineligible for EI. Instead, Statistics Canada conducts the Labour Force Survey, interviewing people to find out their employment status and then estimating the unemployment rate for the whole country. During the second half of every month, Statistics Canada analysts survey about 50,000 households, analyze the responses, and report the results. The most widely publicized number from this survey is the unemployment rate, but the survey covers much other information; for example, shifts of employees from one industry to another, hours worked, and demographic information about employees including age, sex, marital status, education level, and province or territory of residence. Answer the following questions: a) State the objectives of the survey. b) What is the population of interest?

c) What are the parameters for this survey? d) Why might it be difficult to select a simple random sample from this sampling frame? e) What sampling technique would you use to ensure that we have a representative sample of people from each province and territory and from the demographic groups described above? Question #3: [8 marks] Sampling Distributions, Central Limit Theorem, the Normal Distribution/Model Five hundreds ball bearings have a mean of 5.02 grams (g) and a standard deviation of 0.30 g. a) Find the probability that a random sample of 100 ball bearings chosen from this group will have a combined weight between 469 and 500 g? b) Find the probability that a random sample of 100 ball bearings chosen from this group will have a combined weight more than 510 g? c) Repeat a) only with a sample size of 25 instead of 100. d) What impact does the sample size have on your results? Explain the reason why. Question #4: [10 marks] Linear combinations of correlated random variables A study on job satisfaction (X) and the number of years of experience (Y) was conducted with Public Service employees from one of the Canadian Government Department. The study found out the following joint probabilities. Level of satisfaction x i Number of years of experience y j f(x i y j ) 1 1 0.09 2 3 0.10 3 6 0.22 4 9 0.32 5 12 0.27 a) Find the expected value for the number of years of experience from the employees of this Department. b) Find the standard deviation for the level of satisfaction from the employees of this Department. c) Find the correlation coefficient between X and Y. d) More recent studies made it possible to develop a performance index, which allows to measure the level of performance (P) based on level of satisfaction and number of years of experience. It is expressed by the following function: P = 0.7X + 0.3Y. Find the expected value and standard deviation for this level of performance (P) index.

Question #5: [4 marks] Sampling Distribution for Proportions A market researcher for a provider of phone accessories wants to know the proportion of customers who own cars to access the market for a new phone car charger. A survey of 500 customers indicates that 76% own cars. a) What is the standard deviation of the sampling distribution of the proportion? b) How large would the standard deviation have been if the researcher had surveyed only 125 customers (assuming the proportion is about the same)?

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