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sadiejane1125
14.04.2020 •
Mathematics
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.
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Ответ:
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:![\sigma \leq 17500](/tpl/images/0599/2927/08298.png)
Alternative hypothesis:![\sigma 17500](/tpl/images/0599/2927/860f3.png)
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"
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:![\sigma \leq 17500](/tpl/images/0599/2927/08298.png)
Alternative hypothesis:![\sigma 17500](/tpl/images/0599/2927/860f3.png)
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.
Ответ:
Justification of step A: common denominator
Justification of step B: multliplication property of equality
Step-by-step explanation:
i got it right.