29 Nov Statistical Applications Project for MA135? You are doing research on balance and fitness. To complete this research you will need a watch with a second hand. Identify a
Statistical Applications
Project for MA135
You are doing research on balance and fitness. To complete this research you will need a watch with a second hand. Identify a random sample of n = 12 men and n = 8 women. You must answer this question: How do you establish that this sample is truly random?
Have each subject perform the following task:
a) Have the subjects stand with their hands at their side, raise one knee, cross their ankle over the other knee, squat and bring their hands palms together in front of their chest. Time the subject until they put their foot back down on the floor.
b) Ask the following questions:
i) How many days per week do they exercise?
ii) What is their favorite exercise?
You will analyze your data and compute the following statistics for each group:
1) The Mean and standard deviation of the number of seconds the subject stayed balanced
2) The Median number of days per week exercised
3) The Mode of the favorite exercise
4) The 90% confidence interval of the mean
5) Construct a complete hypothesis test and determine if the two groups have significantly different balance using α = 0.05.
Write a one page introduction to your research, discuss how you selected your sample (is it a random sample?), and write a one page conclusion. Present your data in an organized manner.
Research Project Rubric
Organization: Maximum of 10 points
Overall report is well organized, with a cover page, introductory page, discussion of sampling, all data is shown, statistics are clearly presented, and conclusion page.
(Points are deducted for presentation, missing information).
Statistics: Maximum of 40 points
Mean for each group is correct (8 points)
Standard deviation for each group is correct (8 points)
Median for each group is correct (8 points)
Mode for each group is correct (8 points)
Confidence interval of the mean for each is correct (8 points)
Hypothesis Test: Maximum of 30 points
Null and Alternate Hypothesis are stated correctly (6 points)
Critical t value is correct (6 points)
Computation of the t statistic is correct (6 points)
Decision regarding the hypothesis is correct (6 points)
Conclusion regarding the hypothesis is correct (6 points)
Writing: Maximum of 20 Points
Overall writing is thorough with correct grammar, punctuation,
spelling, and capitalization.
(Points are deducted for quality and mechanics).
Extra Credit: Maximum of 5 points
Graphics, graphs… Wow me!
After downloading the excel data generator, please take a screen shot like below then attach it on the first page of the project.
After downloading the excel data generator, please take a screen shot like below then attach it on the first page of the project.
Figure 1Excel data generator
Figure 2
If you do not attach, you will lose 10% of the grade.
After downloading the excel data generator, please take a screen shot like below then attach it on the first page of the project.
Sample Cover page
MA-135(Section #):
Title
Figure 3Picture
Student’s name:
Date: …………….
Professor’s name:
Sample project of MA-135
Write down the name of the project here.
Add your own introduction here (one paragraph)
The data collected from the 12 men & the calculations asking in the project are shown in the table below:
|
Male |
Time in Second(X) |
Number of Days Workout |
Favorite Workout |
|
|
M1 |
Use the number from the excel data generator |
Square the x value from left column for each row below |
Use the number from the excel data generator |
Use the list from the excel data generator |
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M2 |
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M3 |
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M4 |
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M5 |
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M6 |
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M7 |
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M8 |
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M9 |
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M10 |
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M11 |
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M12 |
n = 12 Median= Mode=
Mean (M) = =
SS =
The standard deviation: S = = =
The Standard error of the mean: = = =
Level α = 0.10
df = n-1 = 12-1= 11
t Value (From the chart) = ±1.796
90% confidence interval for the men = M ± CV X
The data collected from the 8 women & the calculations asking in the project are shown in the table below:
Female |
Time in second(X) |
|
Number of Days Workout |
Favorite Workout |
|
FM1 |
Use the number from the excel data generator |
Square the x value from left column for each row below |
Use the number from the excel data generator |
Use the list from the excel data generator |
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FM2 |
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FM3 |
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FM4 |
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FM5 |
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FM6 |
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FM7 |
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FM8 |
n = 8 ∑X = Med= Mode
Mean: M = =
SS =
The standard deviation: S = = =
The standard error of the mean: = = =
Level α = 1-0.90 = 0.10.
df = n-1 = 8-1 =7
t value (From the chart) = 1.895
90% confidence interval for the women= M ±CV (t-value) X
Hypothesis test:
Male Female
= 12 = 8
= use mean from male group = use mean from female group
= use from male group = use from female group
df = + – 2
= 12 + 8 -2
df = 18
Level = 0.05.
1. The null hypothesis ( ) : – = 0
1. The alternative hypothesis ( ) : ≠ 0
1. The critical value : t = ± 2.101
1. The test statistics : Detail calculations
Pooled variance: = = = = 8.23 This is just a sample!
Estimated standard error: = =
= = = 1.31(you will have different answer)
The t statistics: t = = = = -2.48 (you will have different answer)
The test statistics: = -2.48 (you will have different answer)
1. Decision:
Figure 4 Normal curve
Make sure you level the CV and don’t forget to shade the area of the region!
1. Conclusion about the claim: At _____% significant level, the data_______ provide sufficient evidence to ………………………………………………………………..
5
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Sheet1
| Balance Time (sec) | Number of Days Workout | Favorite Workout | ||||
| 1 | Men 1 | 154 | 4 | Legs | 2 | |
| 2 | Men 2 | 56 | 5 | Chest | 3 | |
| 3 | Men 3 | 44 | 1 | Legs | 2 | |
| 4 | Men 4 | 113 | 3 | Chest | 3 | |
| Men 5 | 77 | 3 | Chest | 3 | ||
| Men 6 | 144 | 2 | Arms | 1 | ||
| Men 7 | 39 | 5 | Chest | 3 | ||
| Men 8 | 90 | 7 | Arms | 1 | ||
| Men 9 | 22 | 6 | Chest | 3 | ||
| Men 10 | 85 | 3 | Chest | 3 | ||
| Men 11 | 59 | 2 | Chest | 3 | ||
| Men 12 | 87 | 7 | Arms | 1 | ||
| Women 1 | 95 | 3 | Arms | 1 | ||
| Women 2 | 36 | 1 | Legs | 2 | ||
| Women 3 | 17 | 6 | Chest | 3 | ||
| Women 4 | 102 | 2 | Legs | 2 | ||
| Women 5 | 122 | 7 | Chest | 3 | ||
| Women 6 | 93 | 6 | Legs | 2 | ||
| Women 7 | 61 | 2 | Arms | 1 | ||
| Women 8 | 156 | 5 | Chest | 3 |
Sheet2
Sheet3
