Which transformation represents a reflection over the y = x line?
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Answer:
Step-by-step explanation:
Hello!
The study variable is
X: Lumen of a bulb of the i brand. i=3
There are 3 populations of bulbs, Brand 1, Brand 2 and brand 3.
The objective is to test if the population means are equal.
The study parameters are:
μ₁: population mean lumen of the population of light bulbs of brand 1.
μ₂: population mean lumen of the population of light bulbs of brand 2.
μ₃: population mean lumen of the population of light bulbs of brand 3.
The hypothesis is:
H₀:μ₁= μ₂= μ₃= μ
H₁: At least one of the population means is different.
To test this hypothesis, considering the given information, I'll use an ANOVA test, then the statistic is defined as:
~
Rejection region
This region is always one-tailed (right), the statistic is constructed as the mean square of the treatments divided by the mean square of the error, if the number of F is big, this means that the treatments have more effect over the populations. If the value of F is small, this means that there is no difference between the variability caused by the treatments and the one caused by the residues.
Since there is no significance level specified, I'll use α: 0.05
You will reject the null hypothesis when F ≥ 19.35
To calculate the statistic value you need to calculate the Mean Square of Treatments and the Mean Square of errors:
MSTr= SSTr/DfTr = 599.5/2= 299.75
MSerror= SSerror/Dferror= 4776.3/5= 955.26
F=
= 0.31
At this level the decision is to not reject the null hypothesis.
I hope it helps!