Question

What statistical test is most appropriate if you want to examine whether there is a difference in graduation rates (percentages) between public and private high schools in your state of residence? Assume the data meets the assumptions for a parametric test.

Answer 1

Since there are 2 populations here (private and public schools), and we want to check if the graduation rates are the same, we use a 2 tailed, 2 sample t test.

In this test, take

Let be the the average.graduation rates for private schools.

Let be the the average.graduation rates for public schools.

The Hypothesis:

H0: The graduation rates of private schools is equal to the graduation rates of public schools.(Claim)

Ha: The graduation rates of private schools is different from the graduation rates of public schools.

This is a Two tailed test.

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For pooled Variance:

If s₁/s₂ lies between 0.5 and 2 we used the pooled standard deviation.

The degrees of freedom used is n1 + n2 - 2

The Test Statistic:

The Decision Rule: If tobserved is >tcritical or If tobserved is < -tcritical, Then Reject H0.

Also If the P value is < , Then Reject H0

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For Unpooled Variance:

If s₁/s₂ is less than 0.5 or greater than 2, he degrees of freedom used is

The Test Statistic:

The Decision Rule: If tobserved is >tcritical or If tobserved is < -tcritical, Then Reject H0.

Also If the P value is < , Then Reject H0

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