Consider the matrices -2 -1 1 4 1 A = B = 4 -2 4 -2 -2 4 -2 1 -1 (a) Verify that they are diagonalizable and that they commute.
(b) Find the eigenvalues and eigenvectors of A and verify that its spectrum is nondegenerate. (c) Show that the eigenvectors of A are eigenvectors of B as well.
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Answer:
The test statistic is
Step-by-step explanation:
We are interested in determining whether or not the proportion of the student who experience anxiety during the exam is significantly more than 80%.
At the null hypothesis, we test if the proportion is 80%, that is:
At the alternate hypothesis, we test if the proportion is more than 80%, that is:
The test statistic is:
In which X is the sample mean, is the value tested at the null hypothesis,
is the standard deviation and n is the size of the sample.
80% is tested at the null hypothesis:
This means that
A random sample of 100 students was taken. Eighty-five of the student in the sample experienced anxiety during the exam.
This means that
The test statistic is
The test statistic is