1 Assignment 1 consists of a theory component (1A, worth 80%) and a computer component (1B, worth 20%). The total marks allocated are summarized below. Assignment Grade weight Assignment 1A. Theory component 96 marks 80% Assignment 1B. Computer component 24 marks 20% Total marks 120 marks 100% You must submit Assignment 1A and Assignment 1B together as PDFs, through the appropriate drop box on the course home page. Submit: 1. One PDF solution file (file) entitled Assignment1A containing all your answers to Assignment 1A, presented in the proper order. Your name and student ID number must be at the top of the first page of your solution file. and 2. One PDF solution file (file) entitled Assignment1B containing all your answers to Assignment 1B, presented in the proper order. We suggest that you print the Assignment 1 questions, so that you can conveniently review the questions with their solutions when you prepare for your exams. Computer-oriented Approach to Statistics 1 Assignment 1A. Theory Component Show your work for this component. Where relevant and unless otherwise instructed, keep your calculations and your final answer to at least four decimals. Problem 1. Consumer survey Consider this consumer survey for a family shoe store: Survey For Office Use Only Please check off the boxes that apply to you. Variable 1. Please indicate your marital status. Marital Code married 1 single 2 2. Are you employed outside of the home? Work yes 1 no 2 3. How do you find out about our sales events? Promo newspaper promo 1 radio promo 2 TV promo 3 4. Please estimate how much you spend on shoes per year. $_________ Spend 5. Please indicate your age in years. _________ Age Figure 1. Shoe store survey questions. In the shoe store consumer survey, indicate: a. which variables are qualitative and which are quantitative [5 marks] b. which variables are nominal variables [3 marks] c. which variables are ratio variables [2 marks] d. Name two statistical methods (tools or measures) studied in Unit 1, that would be suitable for analyzing or summarizing the marital status variable. [4 marks] 2 Mathematics 216/ Assignment 1 Problem 2. Oakford Speed Campaign The police service in the small city of Oakford mounted an intensive photo radar campaign to reduce drivers' speeds in school zones. The speed limit in Oakford's school zones is 30 kph. Past records (from before the radar campaign began) indicate that the average recorded speed in Oakford school zones was 34 kph, and that the majority of drivers exceeded this average recorded speed. Having included all the school zones in the city in their photo radar campaign, the Oakford police service recorded the speeds (in kph) of a random sample of 20 drivers from various school zones in Oakford, as follows. 21 44 39 24 24 28 22 44 28 44 34 28 24 23 22 39 34 28 29 26 Figure 1. Recorded speeds. Based on the 20 data values above: a. Compute the mean speed. [2 marks] b. Compute the median speed. [2 marks] c. Determine the modal speed. [2 mark] d. Compute the standard deviation of the 20 speed values. [6 marks] e. Of the drivers recorded, 25% showed speeds on or below what rate of speed (in kph)? [3 marks] f. Based on a comparison of the mean and media speeds computed in a and b above, comment on the skewness of the distribution of the 20 recorded speeds. [3 marks] g. Construct a frequency distribution of the data, using equal class intervals of 5 (i.e., class width = 5). Make your first class 20 to 25. For each class in your distribution, show the midpoint, the frequency, the relative frequency (in percent), and the less than cumulative frequency. [6 marks] h. Hand-sketch a frequency polygon based on the frequency distribution conducted in g above. [4 marks] i. Based on your sketch of the frequency polygon, determine if the 20 speed values are positively or negatively skewed. How can you tell? [2 marks] j. Would the mean or the median be a better measure of central tendency for the 20 speed values? Explain. [2 marks] k. Compare the mean and the skewness of the recorded speeds after the radar campaign with the mean and skewness of the recorded speeds before the radar campaign. Would you conclude that the photo radar campaign was a success or a failure? Briefly explain. [6 marks] Computer-oriented Approach to Statistics 3 Problem 3. Monthly Salaries A sample of 100 graduates who completed a 6-month security guard training program reported the following monthly starting salaries (in security guard related employment). Monthly Salary Number of Graduates $1,000-$1,400 1 $1,401-$1,800 11 $1,801-$2,200 14 $2,201-$2,600 38 $2,601-$3,000 36 Total 100 Figure 1. Graduate Salaries. a. Compute the (approximate) mean monthly starting salary. [4 marks] b. Compute the (approximate) standard deviation of the monthly starting salaries. [6 marks] c. Hand-sketch a relative frequency histogram, using a percentage scale on the Y-axis. Do not be concerned with drawing the graph exactly to scale. Based on the sketch, determine if the distribution of the salaries is positively or negatively skewed. What does the skewness reveal, in terms of the distribution of starting salaries? [6 marks] Problem 4. InfoMart Report InfoMart is a research firm that collects and analyzes information for business firms, government agencies, non-profit organizations, and consumer clients. InfoMart has just completed a report comparing the demographic features of two cities that have similar size populations. In this question, you will examine some of the summary statistics that InfoMart computed with respect to two demographic variables: monthly household income, and age of the homeowner. These summary statistics are presented in the table below. (Homeowner age for Mountainview is not shown in the table, as it is not required to complete this problem.) 4 Computed Statistic Mountainview: Household inc. Rivercity: Household inc. Rivercity: Homeowner age Mean 4,300 4,300 45 Minimum 0 0 20 Maximum 10,200 10,200 70 First Quartile (Q1) 1,500 4,000 25 Second Quartile (Q2) 2,000 4,500 50 Third Quartile (Q3) 8,000 4,800 55 Standard Deviation 3,750 100 20 Mathematics 216/ Assignment 1 Figure 1. InfoMart data. a. Determine the median monthly household income for each city as shown in the table above. [2 marks] b. In Rivercity, which variable, income or age, exhibits the greater degree of relative variability? Compute the appropriate statistics. [4 marks] c. In Mountainview, within what range of monthly household income does the middle 50% of households fall? [2 marks] d. Compute the variance for the age variable for Rivercity. [2 marks] e. In Rivercity, 75% of the households surveyed exceed what age? [2 marks] f. In Mountainview, 75% of the households surveyed earned less than what monthly income? [2 marks] Problem 5. Utility Bills The mean monthly utility bill for all households in a mid-sized city is $100, with a standard deviation of $20 per month. The monthly utility bills have a bell-shaped distribution. The Thompson family received a monthly bill of $150. Compute the Thompson family's z-score, and determine if their monthly utility bill would be considered statistically unusual. Briefly explain how your answer relates to the empirical rule. [6 marks] Problem 6. Student Transcript Joe Smith, a student at Metro University, completed the courses Biology 101, Psychology 210, Chemistry 250, and English 200 in the fall semester of 2015. He received the grades transcript below. Fall Semester 2015, Transcript for Joe Smith Course Course Credit (weight) Course Grade Biology 101 45 86 Psychology 210 30 74 Chemistry 250 45 88 English 200 60 77 Figure 1. Transcript Compute Joe Smith's overall average grade (often called grade point average) for the fall semester. [4 marks] Computer-oriented Approach to Statistics 5 Problem 7. Travel Times An employee in a university's parking office wants to consider typical one-way travel times from home to the university for those applying for on-campus parking. The employee randomly selects 25 student parking applications and sees the following one-way travel times (in minutes) from home to the university: 22 65 64 65 54 45 35 57 47 46 32 48 68 45 55 45 54 52 66 52 55 36 61 69 63 Figure 1. Travel times. Construct a finished stem-and-leaf plot, with the stems ranging from 2 to 6. [4 marks] Assignment 1B. Computer Component As you work through each computer problem, use StatCrunch to generate all computer-related solutions. Do not round off the results you get from StatCrunch. Make sure that, for each computer problem, you copy and paste the output generated by StatCrunch (as is) as requested, into a single word processing file called Assignment1B. Use a word processing program that allows you to convert to a PDF file after you have completed all your solutions. Be sure to type the appropriate problem subheading (e.g., Problem 8a) before you copy and paste the related StatCrunch output or type solutions to the related interpretation questions in the Assignment1B word processing file. Each time you make a change to a StatCrunch file or word processing file, be sure to save the file. Problem 8. WR Rodeo: Create and Recode Data File WR Rodeo is a world-renowned rodeo held annually in a western Canadian city. It is a week-long event that provides a variety of rodeo and social events, games and rides, gift shops, and fast food outlets to its attendees. The rodeo sells an advance discount package that gives event discounts on rodeo events and related entertainment activities. The municipal government hosting the rodeo presented the survey below to people attending the rodeo. 6 Mathematics 216/ Assignment 1 Please circle the survey code or fill in the numeric values that apply to you below. Variable 1. Please indicate where you live. Home Text Code Rural Area 1 Urban Area 2 2. Do other members of your family attend rodeo-related events, functions, and entertainment activities? Family Code Yes 1 No 2 3. Did you purchase the rodeo's advance discount package? Discount Code Yes 1 No 2 4. Which one of the following do you feel is most effective in attracting attention to WR Rodeo's various events and functions? Promo Code Newspaper promo 1 Radio promo 2 TV promo 3 5. How much do you (and your family) spend each day on rodeo-related events? Spend $ _____ 6. During rodeo week, how many rodeo-related events, functions, and/or activities do you or other family members attend? Attend _______ 7. Please indicate your monthly family income before taxes. Income $ ______ 8. Please indicate your age. Age ______ Figure 1. Survey questions. Computer-oriented Approach to Statistics 7 The responses of 25 regular attendees who responded to this survey are given in the table below. 8 Resp# Home Family Discount Promo Spend Attend Income Age 1 1 1 1 2 350 13 7400 45 2 1 1 1 1 400 14 8600 31 3 2 2 2 1 150 2 3600 62 4 1 2 1 1 300 12 8700 32 5 2 2 1 1 100 3 8800 33 6 2 1 2 2 75 2 5300 53 7 2 2 2 2 100 3 4100 64 8 1 1 1 1 500 13 8300 34 9 1 1 1 1 500 15 8800 35 10 2 2 2 1 100 3 4400 65 11 1 1 1 1 200 10 6500 51 12 1 1 1 2 350 10 6400 52 13 2 2 2 1 50 2 5200 54 14 1 1 1 1 300 10 7200 44 15 1 1 1 1 450 12 7400 43 16 1 2 1 2 450 14 7900 37 17 2 2 2 1 50 2 3400 72 18 1 1 1 1 300 10 7300 42 Mathematics 216/ Assignment 1 19 1 1 1 2 200 8 6800 47 20 2 2 2 1 150 4 5200 55 21 2 2 2 1 100 2 4200 52 22 1 1 1 3 400 12 7900 41 23 1 1 1 1 500 14 8700 36 24 1 1 2 1 600 15 8750 38 25 2 2 2 3 150 4 6900 46 Figure 2. 25 Responses to WR Rodeo Survey: File WR Rodeo a. Create a StatCrunch data file called Rodeo, which contains the 25 customer responses to the WR Rodeo survey entered in the data table (based on Figure 2). Do not include the first column, Resp# data, in the StatCrunch data table. In the file, create the variables: Home, Family, Discount, Promo, Spend, Attend, Income, and Age. After entering all the survey data, save the data file as Rodeo in your My Data Folder on the StatCrunch website. Then sign out of StatCrunch. Open a new word processing file that can later be saved in PDF format. In this file, type the title: Assignment1B. In the line below the title, type Problem 8a. Save this file as Assignment1B. Keep the file open as you proceed to the next step. Open the StatCrunch data file Rodeo from your My Data folder in StatCrunch. Copy and paste all the quantitative variables, and the first five data values for each quantitative variable, directly from the StatCrunch data table to your word processing file Assignment1B, under the subheading Problem 8a. Remember to save each time you update this file. [1 mark] b. Open the StatCrunch file Rodeo, which you created in 8a, and recode each qualitative variable based on the table below. After you have recoded the variables displayed in Figure 3, resave the StatCrunch Rodeo file under the same name. Before you analyze the qualitative variables in the Rodeo survey, it will be useful to recode the responses for these variables to recognizable text descriptions. For example, for Home responses, recode 1 to Rural and 2 to Urban in a new column called Recode(Home) , as described in Figure 3 below. Computer-oriented Approach to Statistics 9 Recode values for the qualitative variables in the Rodeo file Variable Original Code Home Family Discount Promo New Code 1 Rural 2 Urban 1 Yes 2 No 1 Yes 2 No 1 Newsp 2 Radio 3 TV Figure 3. Recoding variables. Copy and paste all the recoded variables along with the first five data values (for each of the recoded variables) from the StatCrunch data table to your word processing file Assignment1B, under the subheading Problem 8b. [1 mark] Problem 9. WR Rodeo: Modal Response Open the StatCrunch data file Rodeo. a. Use StatCrunch to determine the modal response for each of the qualitative variables Family, Discount, and Promo. Copy and paste the StatCrunch Summary Statistics table (which displays the mode) to your word processing file Assignment1B, under the subheading Problem 9a. [1 mark] b. Under the subheading Problem 9b, type the mode for Family, Discount, and Promo. Interpret the results in terms of the appropriate recoded values. [1 mark] 10 Mathematics 216/ Assignment 1 Problem 10. WR Rodeo: Pie Chart Open the StatCrunch data file Rodeo. a. Use StatCrunch to create a pie chart for the variable Recode(Home). Each slice of the pie should display each Home variable category's relative frequency (% of total responses). Copy and paste the pie chart from StatCrunch to your word processing file Assignment1B, under the subheading Problem 10a. [1 mark] b. Based on the pie chart, type the Recode(Home) variable category that most frequently occurred, under the subheading Problem 10b in the Assignment1B word processing file. [1 mark] Problem 11. WR Rodeo: Pareto Chart Open the StatCrunch data file Rodeo. a. Use StatCrunch to create a Pareto chart summarizing the responses to the variable Recode(Promo) regarding the effectiveness of different types of media promotions. Order the variable categories by count descending. Copy and paste the StatCrunch Pareto chart to your word processing file Assignment1B, under the subheading Problem 11a. [1 mark] b. What does the Pareto chart you just created suggest about which types of media promotions should be used in the future? Explain. Type your explanation into your word processing file Assignment1B, under the subheading Problem 11b. [1 mark] Problem 12. WR Rodeo: Contingency Table Open the StatCrunch data file Rodeo. a. Use StatCrunch to create a contingency table that examines the relationship between the two variables Recode(Home) and Recode(Discount). Select Recode(Home) as the row variable and Recode(Discount) as the column variable. Display the Row percents in the table. Copy and paste the contingency table from StatCrunch to the word processing file Assignment1B, under the subheading Problem 12a. [1 mark] b. Under the subheading Problem12b, type the relationship that appears to exist (if any) between the variables Recode(Home) and Recode(Discount), focusing on the appropriate row percents. [1 mark] Problem13. WR Rodeo: Frequency Table Open the StatCrunch data file Rodeo. a. Use StatCrunch to create a frequency table summarizing the responses to the Income survey question. The frequency table should have six bins (classes) with a starting value of 3000 and a fixed bin width of 1000 where each bin includes the left endpoint. The frequency table should display Frequencies, Relative frequencies, and Cumulative relative frequencies. Copy and paste the StatCrunch frequency table to your word processing file Assignment1B, under the subheading Problem 13a. [1 mark] Computer-oriented Approach to Statistics 11 b. What income category (class) is the most frequent? Type your answer in the word processing file Assignment1B, under the subheading Problem 13b. [1 mark] c. Interpret the relative frequency of the fourth class. Type your answer in the word processing file Assignment1B, under the subheading Problem 13c. [1 mark] d. Interpret the cumulative relative frequency of the fifth class. Type your answer in the word processing file Assignment1B, under the subheading Problem 13d. [1 mark] Problem14. WR Rodeo: Histogram Open the StatCrunch data file Rodeo. a. Use StatCrunch to create a histogram summarizing the responses to the Income survey question. The histogram should have 6 bins (classes) with a starting value of 3000 and a fixed bin width of 1000. The histogram should display the relative frequency of each class. Copy and paste the histogram to your word processing file Assignment1B, under the subheading Problem 14a. [1 mark] b. Based on the histogram for Income, comment on the skewness of the income data. What does this skewness suggest about the income distribution of those who attend the rodeo? Type your answer under the subheading Problem 14b. [1 mark] Problem15. WR Rodeo: Mean, Median, Standard Deviation, Variance, and Coefficient of Variation Open the StatCrunch data file Rodeo. a. Use StatCrunch to determine the mean, median, standard deviation, variance, and coefficient of variation for both variables, Income and Age, in the same StatCrunch table. Copy and paste the Summary Statistics table displaying all these statistics to your word processing file Assignment1B, under the subheading Problem 15a. [1 marks] b. Based on the results in Problem 15a, which variable, Income or Age, displays a greater degree of relative variability? Type your answer and explanation under subheading Problem 15b. [1 mark] c. Based on the results in Problem 15a, which variable, Income or Age, displays a slightly positive skew? Type your answer and explanation under subheading Problem 15c. [1 mark] Problem16. WR Rodeo: Daily Amount Spent Open the StatCrunch data file Rodeo. a. Use StatCrunch to compute the mean and standard deviation daily amount spent for each of the Home subsets: rural and urban attendees. In other words, compare the mean and standard deviation amount spent per day during Rodeo week by rural vs. urban attendees at the rodeo. Copy and paste the Summary Statistics table to your word processing file Assignment 1B, under the subheading Problem 16a. [1 marks] b. Which Home category tends to spend more per day during Rodeo week? Type your answer in the word processing file Assignment1B, under the subheading Problem 16b. [1 mark] 12 Mathematics 216/ Assignment 1 Problem17. WR Rodeo: Box-and-whisker Plots Open the StatCrunch data file Rodeo. a. Use StatCrunch to create two box-and-whisker plots comparing the number of events, functions, and activities attended by rural attendees (subset of variable Recode(Home)) to WR Rodeo with the number of events, functions, and activities attended by urban attendees (subset of variable Recode(Home)). Copy and paste the box-and-whisker plots to your word processing file Assignment1B, under the subheading Problem 17a. [1 marks] b. Which subset of the variable Home tends to attend a greater number of events, functions, and activities during Rodeo week? Type your answer in the word processing file Assignment1B, under the subheading Problem 17b. Hint: Move your mouse pointer over each box plot in StatCrunch to display a pop-up window that shows the median for each boxplot. [1 mark] c. Based on the box-and-whisker plots, type the values for the first quartile, third quartile, and interquartile range for the number of events, functions, and activities attended by the rural attendees, under the subheading Problem 17c in the Assignment1B file. [1 mark] Computer-oriented Approach to Statistics 13