1. The Department of Labor in the United States is conducting a study to understand the commuting patterns of working individuals in two of its largest employment hubs: Los Angeles and New York. The study focuses on the commuting times to work for 40 randomly selected individuals in each city over one month. As a statistics student, your task is to analyze this dataset and provide an insightful statistical report. Your report should support your findings using statistical techniques and visual representations. EVERET New York Commuting Times 45 8 8 15 15 30 30 90 20 35 90 30 75 15 20 45 75 60 40 90 45 15 45 60 60 30 10 45 60 30 30 60 60 40 75 30 30 45 20 60 25 10 F2 Los Angeles Commuting Times 30 20 45 30 60 60 30 30 5 LO 45 60 60 69 25 60 25 60 25 25 10 10 60 60 15 20 40 60 60 45 10 10 60 15 60 330 66 20 23 45 15 25 45 15 30 30 80 25 20 30 15 30 # 3 @ 80 F3 000 000 F4 $ 4 % 5 F5 MacBook Air F6 & F7 * F8 6 7 8 9 E R T Y D F G H F9 19 F10 F11 O P J K L V = { 2 3 5 a. [2 points] Are the data discrete or continuous? How do you know? 6 7 b. [4 points] Construct a dot-plot graph for the commuting times of the 40 individuals from Los Angeles. Explain how this visual representation helps in understanding the distribution of commuting times. Paste the dot-plot graph here. I recommend using Stapplet. I EVERETT c. [3 points] Identify the mean, median, and sample standard deviation for Los Angeles commuting times. Round to one decimal place, and use a proper statistical notation. % # 80 F3 3 $ 4 000 F4 55 F5 Macbook A F6 % & 5 6 7 E R T Y F7 *8 F8 9 F9 O F10 F11 D F G H J K L P } [ d. [10 points] Create box plots for the commuting times in Los Angeles and New York, using the same scale for both. Use the 5-number summary to describe the spread of commuting times in each city. Look for any similarities or differences between the two cities. Based on your box plots and the spread of data, discuss which city has higher commuting times and how this information could be important for making decisions about city planning and transportation. List the 5-number summary for each data, and label the boxplots correctly. Note: Use this website for the boxplots. Round your data to the nearest integer. I EVERETT e. [5 points] Are there any potential outliers? List the value(s) that could be outliers. Use a formula to check the end values to determine if they are potential outliers. 80 F3 f. [6 points] Calculate the range, interquartile range, variance, and standard deviation of the commuting times for each city. Discuss what these measures tell you about the reliability and consistency of commuting times in Los Angeles and New York Round the numbers to one decimal place 000 000 F4 F5 45 MacBook Air F6 # $ % & 3 4 5 6 7 29 E R T Y F7 F8 8* 9 F9 O F10 D F G H J K L V P F11 + || [ g. [4 points] Discuss the importance of random sampling in this study. What potential sources of bias could affect the validity of the study's findings? How might the Department of Labor mitigate these risks? h. [6 points] Use the commuting time data for New York to find the city's 10th and 90th percentiles. Explain what these percentiles tell you about the usual commute times in New York. How do these percentiles help you understand the spread and typical values of commuting times? Must show tour work; unsupported answers get no credit. EVERETT COMMUNITY COL 80 F3 i. [4 points] Given the commuting time data for New York, calculate the percentile rank P for an individual whose commute time is 45 minutes. Discuss what this percentile rank indicates about this individual's commute time compared to the rest of their city's population. 000 000 F4 # $ % 3 4 5 F5 MacBook Air F6 & F7 * F8 FB 69 F9 6 7 8 9 O E R T Y U F10 F11 + || O P { [ D F G H J K L M V