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Iowa State University *

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Statistics

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Apr 3, 2024

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Stat 226 Homework1 Submission: via Canvas All Sections Instructions: This homework assignment will consist of two parts. • Part 1: Automated grading/numerical response assessment (3 attempts, highest score kept out of 25 points) • Part 2: Free response assessment (1 attempt, graded offline). The free response questions will be extra credit. We have provided all JMP output within this homework to give students a little more time to get familiar with JMP. Unless indicated otherwise, answers are automatically graded in Canvas and should be submitted in Part 1 of the assignment. If a question requires an answer in free response format, it will be identified with the words “Free response submission” at the beginning of the question. These answers should be submitted in Part 2 of the assignment. 1. Job-sharing is an innovative employment alternative that originated in Sweden and is becoming popular in the United States (for example, in 2001, 26% of companies in the U.S. offered it as a flexible work option). Firms that offer job-sharing plans allow two or more persons to work part-time, sharing one full-time job. For example, two job-sharers might alternate work weeks, with one working while the other is off. Job-sharers never work at the same time, and may not even know each other. Job-sharing is particularly attractive to working mothers and to people who frequently lose their jobs due to fluctuations in the economy. In a recent survey of 1,035 major U.S. firms, approximately 23% offer job-sharing to their employees. For each of the questions, select the correct answer from choices i. through xi. listed below. (a) What is the population of interest for the survey? (b) What is the variable measured for the survey? (c) What is the sample selected for the survey? (d) What is the parameter for the survey? (e) What is the statistic for the survey? Answer choices: i. All major U.S. firms. (a) ii. All major firms in the world. iii. Whether a company offers job-sharing or not. (b) iv. The 1,035 major U.S. firms surveyed. (c) v. The percentage of all U.S. major firms which offer job-sharing to their employees. (d) 1
vi. The percentage of the 1035 major firms surveyed which offer job-sharing to their employees. (e) vii. 26%. viii. The percentage of all U.S. major firms which employ working mothers. ix. All workers in the U.S. who have participated in the job-sharing program. 2. State Unemployment. The Bureau of Labor Statistics randomly surveys Iowa residents (16 & older) each month to get a representation of the statewide unemployment rate. These surveys help to estimate the number of individuals 16 and older who are employed, unemployed, or not in the labor force. The unemployment rate is calculated by taking the number of individuals who are reportedly unemployed and dividing it by the total work force (unemployed + employed). Individuals who are classified as “not in the labor force” will NOT be included in this calculation. 2,300 randomly chosen Iowa residents (16 & older) were given this survey in January of 2018. Of the survey respondents, 276 were classified as “not in the labor force,” 57 were classified as “unemployed,” and 1,967 were classified “employed.” For each of the questions, select the correct answer from choices i. through viii. listed below. (a) What is the population of interest? (b) What is the sample? (c) What is the parameter? (d) What is the statistic? Answer choices: i. All people living in Iowa in January of 2018. ii. The unemployment rate for all Iowa residents who are 16 & older. iii. The 276 Iowa residents (16 & older) classified as “not in the labor force.” iv. 2.8% or (57 classified as “unemployed”) ÷ (57 classified as “unemployed” + 1,967 classified as “employed”). (d) v. All Iowa residents who are 16 & older in January of 2018. (a) vi. 2.5% or (57 classified as “unemployed”) ÷ (2,300 residents surveyed). vii. The unemployment rate for all Iowa residents who are 16 & older in January of 2018. (c) viii. The 2,300 randomly chosen Iowa residents (16 & older) in January of 2018. (b) 3. What will happen to the U.S. Housing Market? At the beginning of the Fall 2007 semester we asked Stat 226 students to predict the behavior of the U.S. Housing Market. Students were asked the following question: What do you think, will the average U.S. Housing Price decrease within the next 5 years? Note that the average U.S. Housing Price in 2007 was $313,600. Because a survey was handed out during lecture, we were able to collect all responses. For a 2
random sample of students the responses are saved in a .JMP file called Responses- HousingMarket.jmp . Use these data and JMP to answer the following questions. (a) Free response submission. Construct a pie chart of the data. 1 Export the pie chart and save it as an image file, such as a .png or .jpeg file and upload it to Canvas. The pie chart you submit should be the same as shown below. on a PC: You can do this in JMP by first clicking Ctrl+S to save the image file. Make sure to save the file as a .png, .jpeg or .pdf, for example, but not as a .jrp file ! on a Mac: You can do this in JMP by first clicking on the pie chart window itself. Then choose File = ⇒ Export . From the prompted list of options choose image and save the image locally to your computer. Based on the information in the pie chart answer questions 3b-3d. (b) What percentage did not believe the housing marked would decrease within the next 5 years (either unsure or thought it would increase)? 25.9 (c) What type of variable is the variable of interest, “Will Price Decrease”? Answer choices: i. Numerical (quantitative) variable ii. Nominal categorical (qualitative) variable iii. Ordinal categorical (qualitative) variable (c) (d) If you answered “Categorical” in the previous question, how many categories does the variable of interest consist of? If you answered “Numerical”, what is the range of values the variable can take? 3 (e) If we recorded the average U.S. Housing Price every month for the next year, what graphical display is most appropriate to display the data? ( Hint: The answer is in the lecture notes, Module 1, Chapters 1–3.) Histogram 1 Create a pie chart as follows: In JMP choose Graph Builder and select the pie chart symbol from those appearing on the top right. Next, select the variable of interest and drag it to the X-axis in the graph. You can elect to add labels (i.e. change the Label tab to Label by value ) such as the total number of individuals in a category ( Summary Statistics N ). If you prefer to show percentages, you could change the Label tab to Percent of Total value . 3
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