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Chapter Week 10 Tutorial activities

6540 Chapter Notes - Chapter Week 10 Tutorial activities: Skewness, Yogurt, Control ChartPremium

24 pages48 viewsFall 2018

Department
University of Canberra
Course Code
6540
Professor
Dr Sumaira Qureshi
Chapter
Week 10 Tutorial activities

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ChildrenCereal AdultsCereals Step 0: info & Assumptions
40.3 20
55 30.2
45.7 2.2
43.3 7.5
50.3 22.2
53.5 16.6 Descriptive Statistics
43 14.5 ChildrenCereal
44.2 21.4
44 3.3 Mean
47.4 6.6 Standard Error
44 7.8 Median
33.6 10.6 Mode
55.1 16.2 Standard Deviation
48.8 14.5 Sample Variance
50.4 4.1 Kurtosis
37.8 15.8 Skewness
60.3 4.1 Range
46.6 2.4 Minimum
3.5 Maximum
8.5 Sum
10 Count
1
4.4
1.3 Conditions for Inference
8.1 (1) Randomization: assume random samples
4.7 (2) Normalization: not quite satisfied as the distribution of adult cereals is not sym
18.4 (3) Independence: safely assume two independent samples
Conclusion: Not all conditions are met, thus the test of significance wi ll be an
approximation at best.
Challenge:
Hypothesized value:
Step 1: Hypothesis Design
Challenge:
Hypothesized value:
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𝐿𝑒𝑑 !πœ‡&!𝑏𝑒 !π‘‘β„Žπ‘’!π‘‘π‘Ÿπ‘’π‘’!
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Step 2: Test Stastic
t-Test: Two-Sample Assuming Unequal Variances
Mean
Variance
Observations
Hypothesized Mean Difference
df
t Stat
P(T<=t) one-tail
t Critical one-tail
P(T<=t) two-tail
t Critical two-tail
Step 3: P-Value & Decision Rule
Decision: Reject Ho
Step 4: Conclusion
Based on the given data, we have strong evidene to reject Ho.
What this means is that based on the given data, we have strong evidence
that there is difference in mean % of sugar content between adult and child cereals.
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π‘£π‘Žπ‘™ 𝑒𝑒 !
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ChildrenCereal AdultsCereals
46.85 Mean 10.36666667
1.555787214 Standard Error 1.476443714
46.15 Median 8.1
44 Mode 14.5
6.600646136 Standard Deviation 7.67182658
43.56852941 Sample Variance 58.85692308
0.09568132 Kurtosis -0.030332905
0.093605803 Skewness 0.79700637
26.7 Range 29.2
33.6 Minimum 1
60.3 Maximum 30.2
843.3 Sum 279.9
18 Count 27
(1) Randomization: assume random samples
(2) Normalization: not quite satisfied as the distribution of adult cereals is not sym
(3) Independence: safely assume two independent samples
Conclusion: Not all conditions are met, thus the test of significance wi ll be an
Is there a difference in mean sugar content between adult & children cereals?
Is there a difference in mean sugar content between adult & children cereals?
(2 tailed test)
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π‘ π‘’π‘”π‘Žπ‘Ÿ!%!
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π»π‘Ž
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!!!πœ‡&
βˆ’
πœ‡2β‰  0!!
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