STats_Problem_Set_1

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Feb 20, 2024

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Problem #1 According to the latest census, the height of the Canadian women population is distributed normally, with the following population characteristics: Mean height: 164.4cm Standard deviation: 12.5cm a) Based on this information, give the range (interval) of heights that covers 90% of women across Canada. b) What is the share of the women population who are taller than 200cm? Problem #2 A policymaker is tasked with evaluating an income supplement program for low-income adults after the first two years of the program being in place. The evaluation aims to investigate if the program is functioning as planned, and what adjustments may be warranted, if any. A survey is conducted across a randomly selected sample of 90 individuals currently participating in the program. The following presents the results obtained for one indicator: the age of the selected individuals. a) Create a histogram, either by hand or by using some other application such as Excel, using the following categories of ages: 18-25, 26–35, 36–45, 46–55, 56–65, 66–75, 76–85 and 86+. b) The sample mean for the age question was 52, which is much older than the mean age for the entire Canadian population (42). Based on this information, the policymaker concludes that the bulk of the low- income population targeted by the program is considerably older than the general population, which may require adjustments in the program to better adapt it for people aged 50 and over. Do you agree with this interpretation of the data? Briefly state why (max 150 words).

c) Build a confidence interval for the mean age in the population represented by this sample, with a 95% confidence level. d) What does the confidence interval tell us for the future of the program? For instance, would it be a good predictor for the average age of the population participating in the program when the next evaluation is conducted in three years? Max 150 words. Problem #3 A researcher conducts a survey to estimate a population’s take on various issues. Each question provides a statement presenting a position on the issue, and the respondent must answer on a Likert scale: -2 (completely disagree) -1 (partially disagree) 0 (neutral) +1 (partially agree) +2 (completely agree). a) To do their estimations for population parameters, the researchers build confidence intervals for the average answer to each question. Given that the answer scale is narrow, they would like to make sure that the width of the interval is within 0.2 points on the [-2;2] scale. However, they also had an approximate sample size in mind, based on practical considerations. In these circumstances, the sample size and targeted width of the interval would require an 80% confidence level, which is much too low. What should they do? Be specific and state why. b) In order to obtain a satisfactory level of confidence, the researchers want to have answers from 4,000 respondents selected randomly from the adult population. After initially selecting 5,000 people (randomly), they obtain 3,500 answers, as the rest of selected respondents decline to participate. To get an additional 500 responses, they consider selecting 800 more from the population. Do you agree with the strategy? Why? Max 150 words. Problem #4

Select an empirical research study from a peer-reviewed academic journal. Identify one of the main concepts used by the authors and the definition they put forward for that concept, as well as the operationalization they used to assess this concept (i.e., what variables and indicators were used). Provide a short critique of the choice of variables/indicators. In your critique, be sure to address the reliability and validity of the measurement, whether it is discussed explicitly by the authors or not.

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