MAT201 Session Long Project 4

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jvarznaw

Mathematics

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In this assignment, you will continue to collect data for another 5–10 days. Write a paper (1- to 3-page, typed Word document) including all of the following content:

  • Recalculate the mean, standard deviation, and variance.
  • Is your mean increasing or decreasing?
  • Explain the effects of the larger sample size in relation to your data.
  • Do you think the current sample you have is enough to draw an accurate conclusion, or do you need a larger sample?
  • What conclusions can you draw from comparing both sets of data?
Sample Date Driving Time (mins) Departure Time from Home Arrival Time at Work
1 16-Jul 128 3:25 5:33
2 17-Jul 135 4:15 6:30
3 18-Jul 129 4:05 6:14
4 19-Jul 135 4:10 6:25
5 20-Jul 132 4:15 6:27
6 23-Jul 125 3:25 5:30
7 24-Jul 131 4:25 6:36
8 25-Jul 123 4:30 6:33
9 26-Jul 130 4:35 6:45
10 27-Jul 127 4:15 6:22
11 27-Aug 129 4:10 6:19
12 28-Aug 124 4:06 6:10
13 29-Aug 138 4:15 6:32
14 30-Aug 126 4:13 6:19
15 31-Aug 130 4:30 6:40

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MAT201: SLP #1 1 MAT201: Basic Statistics SLP #1 Joseph Wineman Trident University International MAT201: SLP #1 2 Introduction Statistics is the mathematical science that describes the collection, organization and analysis of raw data. It is of particular importance to organizations because it can be used to aid leaders in making informed decisions rather than relying on gut feelings. Data Gathering I live in the thriving Metropolis of Gadsden, Alabama where I worked for the Goodyear Tire and Rubber Company for five years. After much soul searching, I recently decided to make a career change; staying in the manufacturing industry, but trading tires for The HON Company’s office furniture. Along with the career change came a daily commute to and from the plant in nearby Cedartown, Georgia. The commute consists of a 55 mile drive through a combination of state highways, country towns, construction areas, school zones and a time zone change. Not wanting to be late for work, and still having problems dealing with the time change and irregular speed limits during my commute, I have decided to track the amount of time that I spend driving each day from home to work. My desire is to determine the optimal time to leave for work that allows me to maximize the time I can spend sleeping without being late. I will utilize the stopwatch on my iPhone to track the time, in minutes, from the moment that I leave my driveway until the moment that I reach the parking lot at HON Cedartown. Data was recorded for 10 consecutive work days from July 16 to July 27, 2018, and is recorded below. MAT201: SLP #1 Sample Date Jul 16 Jul 17 Jul 18 Jul 19 Jul 20 Jul 23 Jul 24 Jul 25 Jul 26 Jul 27 1 2 3 4 5 6 7 8 9 10 3 Driving Time (mins) 128 135 129 135 132 125 131 123 130 125 Departure Time from Home 3:25 4:15 4:05 4:10 4:15 3:25 4:25 4:30 4:35 3:50 Arrival Time at Work 5:33 6:30 6:14 6:25 6:27 5:30 6:36 6:33 6:45 5:55 Hypothesis From my limited collection of data points, I believe that my commute takes slightly more time if I leave the house later than 4:30am. This is due to the additional town traffic and construction vehicles that are more prevalent as the world around me wakes up. I believe that this issue will only get worse as we transition from fall to summer due to the school zone that will be active on my commute after 7:00 am. For my project, I have identified the independent variable as my departure time from home as it not effected by the other variable, which I have characterized as my commute time. I have labeled my dependent variable as my commute time as it varies due to other factors like my departure times. The statistical tools that will best help me analyze this association are correlation and regression analysis. Correlation analysis can be utilized to examine the strength of a relationship between two, numerically measured, continuous variables whereas regression analysis helps estimate the relationships among variables. Conclusion I need to collect more data in order to best represent my commute time as my sample size is too small (n = 10). I must continue to collect and plot data points to ensure that my sample averages display a normal distribution. A larger sample size would minimize any MAT201: SLP #1 4 outliers or anomalies which would skew my data. The larger sample size ensures the normality of data which will provide a better analysis of the sample population. At the end of this study, I will be able to accurately determine the latest time that I can leave house while maximizing the amount of time that I can spend sleeping without being late for work. MAT201: SLP #2 1 MAT201: Basic Statistics SLP #2 Joseph Wineman Trident University International MAT201: SLP #2 2 Below is the data that was collected regarding my commute from Gadsden, Alabama to The HON Company, located in Cedartown, Georgia. The commute consists of a 55 mile drive across multiple counties, through various small towns and includes a time zone change as I cross the state border from Alabama into Georgia. The data was recorded using the stopwatch function on my iPhone and took place over ten consecutive work days from July 16 to July 27, 2018. Date Driving Time (mins) Departure Time from Home Arrival Time at Work 1 Jul 16 128 3:25 5:33 2 Jul 17 135 4:15 6:30 3 Jul 18 129 4:05 6:14 4 Jul 19 135 4:10 6:25 5 Jul 20 132 4:15 6:27 6 Jul 23 125 3:25 5:30 7 Jul 24 131 4:25 6:36 8 Jul 25 123 4:30 6:33 9 Jul 26 130 4:35 6:45 10 Jul 27 125 3:50 5:55 Sample 1. Calculate the mean, median, and mode of your collected data. Show and explain your calculations. 123 125 125 128 129 130 131 132 135 a. Mean: Sum all 10 trips or 1293 / 10 = 129.3 b. Median: Average of 129 and 130 = 129.5 c. Mode: The Modes are 125 and 135 135 MAT201: SLP #2 3 2. Are these numbers higher or lower than you expected? Explain. These numbers are much higher than I expected. When I accepted the new job with the HON Company, I thought long and hard about the commute time. Ultimately, I accepted based on the fact that the plant was only 55 minutes away from my home. Actually recording the data, and grouping it in such a way to see the central tendencies, I am actually quite shocked by the information here. However, I do enjoy my work there, so the commute is not a deterrent. 3. Which of these measures of central tendency do you think most accurately describes the variable you are looking at? Provide your justification. I think the mean most accurately describes the variable I am observing. The range of data is fairly tight across the 10 samples and fairly evenly distributed. If I were to drop the lowest outlier, the mean and the median would then be 130, which is less than one integer away from their current values. So, based on my recorded data, it is reasonable for me to expect my commute to last 130 minutes, or 2 hours and 10 minutes. MAT201: SLP #2 4 4. Create a box plot to represent the data, labeling and numerating all 5 points on the box plot. For the plot, you may draw and insert it in your paper as a picture. Make sure it is legible. A B C Solution: A = Minimum - 123 B = 125 C = Median of entire data set – 129.5 D = 132 E = Maximum – 135 A - E = The Range - 12 B - D = The Interquartile Range - 7 D E MAT201: SLP #3 1 MAT201: Basic Statistics SLP #3 Joseph Wineman Trident University International MAT201: SLP #3 2 Below is the data collected in my previous module 1 exercise. The purpose of the data is to determine the amount of time I take to commute from my home in Gadsden, Alabama to my place of work, HON Company whose location is in Cedartown, Georgia. This data will enable me to establish the optimal time am supposed to leave home so that I reach at work in time when all factors put into consideration. Date Driving Time (mins) Departure Time from Home Arrival Time at Work 1 Jul 16 128 3:25 5:33 2 Jul 17 135 4:15 6:30 3 Jul 18 129 4:05 6:14 4 Jul 19 135 4:10 6:25 5 Jul 20 132 4:15 6:27 6 Jul 23 125 3:25 5:30 7 Jul 24 131 4:25 6:36 8 Jul 25 123 4:30 6:33 9 Jul 26 130 4:35 6:45 10 Jul 27 125 3:50 5:55 Sample Frequency Distribution table The frequency distribution is defined as the arrangement or display of outcomes collected according to their sizes or magnitude as per the observations made. Frequency distribution partitions large data into small data of classes showing the number of data values in every class. To construct a frequency distribution table, I will determine the number of classes to use. From the data collected above, I will go with 7 classes because it will give a sufficient summary of the data. Then determine the class width which is given by range/number of classes (Brase, 2013). Subtracting 123 which is the smallest data value from MAT201: SLP #3 3 135 which is the largest data value and dividing the results by a number of classes I get 2 as my class width. Below is the obtained frequency table: class interval 123-124 125-126 127-128 129-130 131-132 133-134 135-136 (f) (X) (FX) (x̄) (X-x̄) (X-x̄)^2 f(X-x̄)^2 1 2 1 2 2 0 2 ∑f=10 123.5 125.5 127.5 129.5 131.5 133.5 135.5 123.5 251 127.5 259 263 0 271 ∑fX1295.0 129.5 129.5 129.5 129.5 129.5 129.5 129.5 -6 -4 -2 0 2 4 6 36 16 4 0 4 16 36 36 32 4 0 8 0 72 ∑ f(X-x̄)^2=152 Standard Deviation Using the Standard deviation formula and figures obtained in the frequency table above SD= √∑ f(X-x̄)^2 =√152/9=√16.88889=4.109 √∑f-1 The standard deviation, therefore, is approximately 4.1 Then: Variance Standard deviation is the square root of the variance and therefore using the standard deviation obtained above, the variance is given by Var=SD^2= (4.1)^2=16.81 Normal Distribution The normal distribution is a symmetrically skewed distribution (Agostino, 2017). Yes it is a normal distribution. This is because the mean of the distribution is 129.5 and 50% of the data values is less than the mean while 50% is greater than the mean. Also using the standard rule that 68%, 95% and 99.7% of the data values should fall within one standard deviation, two standard deviations and three standard deviations of the mean respectively and MAT201: SLP #3 4 using the mean of 129.5and standard deviation of 4.1 as obtained above then 68% of the data values fall within 129.5-4.1 and 129.5+4.1. Implications The results obtained above implies that the process of collecting data hold the properties or aspects of a normal distribution. It also shows that the data collected can be relied upon, that is, the degree of confidence in the results obtained is high. MAT201: SLP #3 5 References Brase, C. H., & Brase, C. P. (2013). Understanding basic statistics. Cengage Learning. D’Agostino, R. B. (2017). Tests for the normal distribution. In Goodness-of-fittechniques (pp. 367-420). Routledge.
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