MATH Elements of Statistics

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Activity6Fall2017.xlsx
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Activity 6

Activity 6—MATH 250
Elements of Statistics—Fall 2017 MATH 250- Elements of Statistics
DUE DATE:  11/16/2017 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 "yournameActivity6". Once complete, submit your answers to this activity by attaching your Excel file through the completion link in the Unit 3 Activity 6 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 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
As discussed in the 11th & 12th chapters of the text, one can use data from a random sample to test a claim or hypothesis about a population. For example, one might want to test the claim that the mean age of all FHSU Elements of statistics students is over 26 years. In this activity, you will apply your understanding of hypothesis testing to actual data—the data collected in Activity 1a of this course. This activity is designed to have you use the cleaned class data to test some claims. This data is given again to the right, and you are encouraged to use the templates given in the Unit 3, Part 1 Excel Guide. If you use a template, just copy & paste the template next to the problem, then make changes to the values, and this will serve as your "work" for that particular problem. 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
NOTE: In all three of these problems below, you are required to demonstrate your analysis process as described in the text, not just the final conclusion. Also, as stated in the resources, there are requirements to applying hypothesis testing that should be checked--requirements that our collected data will actually fail to meet (for instance, the sample should be randomly selected from the population of interest). However, for simplicity of the activity you MAY ASSUME that all requirements for hypothesis testing have been met regarding the data collection process. 18 Female 24.0 164.5 22 160.5 5 Red
19 Male 26.0 184.0 40 169.0 3 Brown
20 Male 27.5 183.5 32 183.0 2 Brown
21 Female 23.5 161.5 29 157.5 5 Brown
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
1. It has been claimed that the average family size of all FHSU Virtual College statistics students is more than 4 people. Using the family size data collected from this year's classes, test this hypothesis--that is does the collected data statistically support this claim? Justify your answer through a formal hypothesis testing procedure with a 0.05 level of significance. Again, necessary claims, calculations, and values must be shown below and to the right. Give your proper/final conclusion below. (Hint: Since the population s.d. is not known, make sure to realize the need to use the t-distribution for testing purposes.) 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
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
H0: 34 Male 30.5 185.5 33 193.5 4 Brown
H1: 35 Female 24.0 164.0 27 168.5 5 Blonde
Sample's Mean (x-bar): 36 Female 25.0 166.0 26 169.0 3 Brown
Sample's S.D. (s): 37 Female 24.5 164.0 26 165.0 3 Brown
Critical Value: 38 Male 24.0 179.0 33 160.0 3 Black
Sample's Test Statistic: 39 Male 26.5 177.0 37 180.0 6 Brown
P-value: 40 Female 27.0 170.0 31 166.0 6 Red
CONCLUSION: 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
51 Female 26.0 178.0 26 175.0 4 Brown
52 Male 28.5 178.0 31 185.5 5 Brown
53 Female 23.0 165.0 31 167.0 2 Brown
2. Past enrollment data indicates that 50% of the students taking elementary statistics at FHSU have brown hair. Is the enrollment in this semester's virtual class significantly different from this claim, as measured statistically? Justify your answer through a formal hypothesis testing procedure on proportions with a 10% level of significance. It is required that you give needed hypotheses and related statistical values below as well as statistical computations to the right (feel free to use the appropriate template from the Excel Guide for Unit 3). Then give a proper final interpretive conclusion below based on the statistical measures calculated and related to the context given. 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
H0: 61 Female 24.0 159.0 40 161.5 7 Brown
H1: 62 Female 26.0 162.5 21 162.5 4 Black
Sample proportion (p-hat): 63 Female 25.5 170.0 28 165.5 6 Brown
Critical Value: 64 Male 28.0 181.0 27 182.5 4 Red
Sample's Test Statistic: 65 Female 22.0 154.0 23 142.0 3 Blonde
P-value: 66 Female 24.0 180.0 31 178.0 4 Brown
CONCLUSION: 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
73 Female 23.0 160.0 23 150.0 2 Brown
74 Male 28.0 177.0 38 184.0 3 Black
3. It has been claimed that the average foot length of adults in the US is less than 26 cm. Does the data of our statistics class support or contradict this claim? Justify your answer through a formal hypothesis testing procedure with a P-value approach using a significance level of your choice. Calculation of and interpretation of the P-value is required on this problem. Give your final conclusion below.
H0:
H1:
Sample's Mean (x-bar):
Sample's S.D. (s):
Sample's Test Statistic:
P-value:
CONCLUSION: