Reference no: EM13968925
Question 1) I went to the Website "Random.org" and asked it to produce 100 random 20-point samples of a Gaussian distribution. Then I pasted the 100 random datasets into Prism and tested each for Normality using Prism's three Normality tests for Gaussian shape. Here are the results.
KS Normality test
Passed Normality test (alpha=0.05)?
Yes Yes Yes No Yes Yes Yes Yes No Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes Yes Yes Yes Yes Yes
D'Agostino& Pearson omnibus Normality test
Passed Normality test (alpha=0.05)?
Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes Yes Yes Yes No Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes Yes Yes No Yes No Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes
Shapiro-Wilk Normality test
Passed Normality test (alpha=0.05)?
Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes Yes Yes Yes No Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes No Yes Yes
1A) Explain why there are 17 tests that conclude that individual data sets are Not Gaussian when we know for certain that they were sampled from a Gaussian distribution? Do the false positives indicate a problem with the random number generator or normality tests?
Question 2)One of the 100 datasets described in the previous question gave a p value of 0.0001 in the D'Agostino Pearson Normality test. These are the values:
27.08300
26.11000
29.04000
26.75600
26.83200
26.28300
26.96700
26.25300
26.65600
26.33800
27.36900
26.35600
26.19100
26.98000
27.34200
26.42800
27.17000
26.41100
27.15200
26.53300
2A) Determine if there is an outlier in the dataset by applying Chauvenet's Criterion.
2B) If any points satisfy Chauvenet'scriertion, remove them and retest the dataset for Normality. Does it now pass the D'Agostino Pearson test? If no points can be rejected, show that that the dataset above fails the Normality test.
Question 3) Propagate errors for the following:
3A) 271 +/- 12 (SD, N=6) x 123 +/- 25 (SD, N=6)
3B) 271 +/- 12 (SD, N=6) / 123 +/- 25 (SD, N=6)
3C) 271 +/- 12 (SD, N=6) + 123 +/- 25 (SD, N=6)
9D) 271 +/- 12 (SD, N=6) - 123 +/- 25 (SD, N=6)
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