Math-Elements of Statistics

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Activity7Fall20171.xlsx
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Activity 7

Activity 7—MATH 250
Elements of Statistics—Fall 2017 MATH 250- Elements of Statistics
DUE DATE:  11/27/2017 Class Data, Fall 2017---CLEANED Student Data
NAME: Individual ID# Gender Foot Length Height Age Armspan Number in Family Hair Color
1 Female 24.0 160.0 31 159.0 3 Red
General Instructions: Please place your name above, then complete the following questions. NOTE: Read the entire document below to get a feel for the activity before continuing. Make sure to save this Excel file often using the filename "yournameActivity7". Once complete, submit your answers to this activity by attaching your Excel file through the completion link in the Unit 3 Activity 7 assignment description in Blackboard. Use the area to the near right in this Excel worksheet when calculating any statistics/parameters. Methods/work used to calculate values in Excel and reach conclusions must be shown in the spreadsheet in order to receive full credit. 2 Male 25.0 172.5 20 177.5 2 Blonde
3 Female 25.5 170.5 28 174.0 4 Brown
4 Male 29.0 185.0 27 192.5 3 Brown
5 Female 28.0 174.5 38 183.0 5 Brown
6 Female 23.0 168.0 38 168.0 3 Red
7 Female 24.5 157.0 21 153.0 4 Blonde
8 Female 21.0 152.0 21 151.0 8 Brown
9 Male 30.5 187.5 29 190.0 5 Black
Overview: 10 Female 23.5 157.5 22 160.0 5 Blonde
In this activity, you will first review graphing qualitative data from Unit 1 and then also review the issues of making a claim about a population from sample data. Next you will apply your understanding of Correlation/Linear Regression, as covered in Chapter 5 of the text, to actual data. The clean class data is given to the right. (Notice that the data is “paired/collated” so if you rearrange the order in one column, you must rearrange all the corresponding row values in the other columns in that same way so that you don’t, for example, mix one person’s age data with another person’s height measure.) We will again assume this data came from a random sample of FHSU students even though we know this to not be true. As in all previous activities, use of Excel in calculating and producing statistical measures is required. 11 Female 23.0 165.0 21 163.0 2 Red
12 Female 23.0 166.0 32 160.0 3 Brown
13 Female 23.0 152.5 35 160.0 6 Brown
14 Female 24.0 165.0 34 165.0 6 Blonde
15 Female 20.0 163.0 20 153.0 4 Blonde
16 Male 26.0 178.0 34 175.5 2 Black
17 Female 24.0 162.5 23 170.5 4 Brown
18 Female 24.0 164.5 22 160.5 5 Red
19 Male 26.0 184.0 40 169.0 3 Brown
1. Complete the following in regard to the hair color category of the data set: 20 Male 27.5 183.5 32 183.0 2 Brown
21 Female 23.5 161.5 29 157.5 5 Brown
a. In the region to the right, make an appropriately labeled frequency table in regard ONLY to the hair color data (for this portion, ignore all other variables in the data set except hair color). Next, extend the frequency table to include a relative frequency column. Finally, create a bar chart graphic from the frequency table. 22 Female 24.5 157.5 22 150.0 3 Brown
23 Male 25.5 179.5 33 184.5 6 Brown
24 Male 27.0 175.0 40 175.0 4 Brown
25 Male 26.0 185.0 31 179.0 3 Brown
26 Female 25.5 170.0 40 169.0 5 Brown
27 Male 25.5 186.0 20 188.0 4 Brown
28 Male 29.0 180.0 47 180.0 7 Black
29 Female 23.0 148.0 39 150.0 5 Brown
b. Directly below, create a statement about “hair color” that the statistical analysis from part a. supports or suggests. Remember this statement is only to be made based on the sampled students' data for the online course as shown in your work in part a. 30 Female 25.0 172.5 23 170.5 6 Brown
31 Female 24.0 167.5 22 162.5 3 Brown
32 Female 24.0 168.0 20 169.0 3 Red
33 Female 24.0 159.0 32 157.0 8 Brown
34 Male 30.5 185.5 33 193.5 4 Brown
35 Female 24.0 164.0 27 168.5 5 Blonde
36 Female 25.0 166.0 26 169.0 3 Brown
37 Female 24.5 164.0 26 165.0 3 Brown
c. Next, create ANY new statement/claim about “hair color” in regard to all students at FHSU (this claim does not have to match the information in the bar chart). Then, briefly discuss whether the chart proves or disproves your statement. Finally, what process would be required to measure statistically whether or not the claim you made here is supported/discounted by the sample evidence? 38 Male 24.0 179.0 33 160.0 3 Black
39 Male 26.5 177.0 37 180.0 6 Brown
40 Female 27.0 170.0 31 166.0 6 Red
41 Female 24.0 170.0 29 155.0 5 Brown
42 Female 22.5 161.0 39 165.5 4 Blonde
43 Female 25.5 171.5 24 142.0 3 Brown
44 Female 25.0 158.0 44 167.0 2 Brown
45 Female 30.5 176.5 36 198.0 1 Brown
46 Female 26.0 158.0 22 160.0 3 Brown
47 Female 23.5 152.5 21 152.5 2 Brown
48 Female 25.0 182.0 24 177.0 4 Brown
49 Female 27.0 167.5 27 167.0 4 Brown
50 Male 27.0 180.0 37 173.0 4 Black
2. Complete the following in regard to the height and armspan variables of the data set: 51 Female 26.0 178.0 26 175.0 4 Brown
52 Male 28.5 178.0 31 185.5 5 Brown
a. In the region to the right, produce a scatterplot of the armspan versus height data (remember this means height runs along the horizontal axis as the independent variable and armspan along the vertical axis as the dependent variable.) Based upon your scatterplot, briefly discuss below your thoughts on whether the “visual” trend between the individuals’ height and armspan appears linear, curvilinear, or has no general trend at all. 53 Female 23.0 165.0 31 167.0 2 Brown
54 Male 28.0 183.0 27 193.0 3 Black
55 Female 23.5 170.5 22 172.0 5 Brown
56 Female 25.5 170.0 27 170.0 3 Brown
57 Female 23.5 170.0 42 150.0 3 Brown
58 Male 24.0 160.0 46 165.0 4 Black
59 Female 25.0 169.5 22 164.5 8 Blonde
60 Female 22.0 151.5 34 156.5 4 Brown
61 Female 24.0 159.0 40 161.5 7 Brown
62 Female 26.0 162.5 21 162.5 4 Black
63 Female 25.5 170.0 28 165.5 6 Brown
b. Complete the following: 64 Male 28.0 181.0 27 182.5 4 Red
65 Female 22.0 154.0 23 142.0 3 Blonde
i. Include the trend line's graph and equation on the scatterplot created in part a. Give the line's equation below and explain within this context what the "x" and "y" variables represent in the equation. 66 Female 24.0 180.0 31 178.0 4 Brown
67 Male 26.0 178.5 35 186.0 6 Brown
68 Male 26.0 178.0 37 176.5 3 Brown
69 Female 24.0 162.5 31 162.5 4 Blonde
70 Female 26.5 165.0 48 169.0 2 Brown
71 Male 31.0 178.0 21 152.0 5 Brown
72 Female 26.0 176.0 21 160.5 3 Brown
ii. Below, explicitly state the slope of your trend line and discuss what the value of the slope signifies in terms of this context. 73 Female 23.0 160.0 23 150.0 2 Brown
74 Male 28.0 177.0 38 184.0 3 Black
c. Determine the value of the correlation coefficient (r) for this paired data. Explain what this value tells you regarding these two variables. Determine the value of the coefficient of determination (r^2) for this paired data. Explain what this value tells you regarding these two variables.
d. Using the predicition equation from part bi. above, predict the armspan of an individual whose height is 170 cm.
e. Finally, critique the statement “since the correlation coefficient is moderately significant” then this means that “being tall causes one to have a longer armspan.” Specifically address the issue of “causation” in relation to statistical correlation.