Claim: High school teachers have incomes with a standard deviation that is more than $17, 500. A recent study of 136 high school teacher incomes showed a standard deviation of $18, 500.
A. Express the original claim in symbolic form.
B. Identify the null and the alternative hypotheses that should be used to arrive at the conclusion that supports the claim.

Part a

For this case the claim is:

And that represent the alternative hypothesis.

Part b: Null and alternative hypothesis

On this case we want to check if the population deviation is higher than 17500, so the system of hypothesis would be:

Null Hypothesis:

Alternative hypothesis:

Calculate the statistic  

For this test we can use the following statistic:

And this statistic is distributed chi square with n-1 degrees of freedom. We have eveything to replace.

Step-by-step explanation:

Notation and previous concepts

A chi-square test is "used to test if the variance of a population is equal to a specified value. This test can be either a two-sided test or a one-sided test. The two-sided version tests against the alternative that the true variance is either less than or greater than the specified value"

represent the sample size

represent the confidence level  

represent the sample variance obtained

represent the value that we want to test

Part a

For this case the claim is:

And that represent the alternative hypothesis.

Part b: Null and alternative hypothesis

On this case we want to check if the population deviation is higher than 17500, so the system of hypothesis would be:

Null Hypothesis:

Alternative hypothesis:

Calculate the statistic  

For this test we can use the following statistic:

And this statistic is distributed chi square with n-1 degrees of freedom. We have eveything to replace.

1. 3. can also be expressed as (22/7)

2. -4.5

3. 3.6

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