The
hue angle color system
assigns an angle for each color from red to violet in the spectrum. Red is 0°
green is 120° and blue is 240°.
A photograph of a
rainbow
taken on Pohnpei was analyzed and the color angles for the rainbow were measured and recorded as seen in the image.
Data: 9;17;24;26;30;36;43;48;52;064;077;088;111;137;165;184;200;217;230;236;239;250;270;303
The data above can be copied and pasted into OpenOffice.org functions to verify the mean and
standard deviation.
Hypothesis test one
For the rainbow hue angle data, the sample size n is 24, the sample mean
x is 127.33,
and the sample standard deviation is 95.89.
Newton put green at the center of his red-orange-yellow-green-blue-indigo-violet rainbow.
On a color wheel green is at 120° .
Test the hypothesis that the population mean μ
hue angle for a rainbow is 120°,
in other words, that the middle of the rainbow is actually green.
Determine the p-value using the t-distribution. p-value = __________
________________________________________ Would we reject the null hypothesis or
fail to reject the null hypothesis that the mean hue angle of 120°
is statistically significantly different from the mean in question three at a 5% level of significance?
__________ If we reject the null hypothesis, what is the risk of a type I error based on the p-value?
__________ What is the maximum confidence level c for which this green is not the middle of the rainbow?
__________ Could green be the middle of the rainbow at an alpha α = 0.05?
Hypothesis test two
On a 360° color wheel the mean hue angle is cyan at 180°.
Test the hypothesis that the population mean μ hue angle for a rainbow is 180°,
in other words, that the middle of the rainbow is actually cyan.
Determine the p-value using the t-distribution. p = __________
________________________________________ Would we
reject the null hypothesis or
fail to reject the null hypothesis that the mean hue angle of 180°
degrees is statistically significantly different from the mean in question three at a 5% level of significance?
__________ If we reject the null hypothesis, what is the risk of a type I error based on the p-value?
__________ What is the largest confidence interval c for which this difference is statistically significant?
__________ Could cyan be the middle of the rainbow at an alpha α = 0.05?
Formulas are written for OpenOffice.org Calc. Replace semi-colons with commas for Excel.
Hypothesis testing for a sample mean versus a known population mean
Statistic or Parameter
Symbol
Equations
OpenOffice
Relationship between confidence level c and alpha α for two-tailed tests