Respuesta :
Answer:
Part a
For this case the claim is:
[tex] \sigma >17500[/tex]
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: [tex]\sigma \leq 17500[/tex]
Alternative hypothesis: [tex]\sigma >17500[/tex]
Calculate the statistic
For this test we can use the following statistic:
[tex]\chi^2 =\frac{n-1}{\sigma^2_0} s^2[/tex]
And this statistic is distributed chi square with n-1 degrees of freedom. We have eveything to replace.
[tex]\chi^2 =\frac{136-1}{17500^2} 18500^2 =150.869[/tex]
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"
[tex]n=136[/tex] represent the sample size
[tex]\alpha[/tex] represent the confidence level
[tex]s^2 =18500^2 [/tex] represent the sample variance obtained
[tex]\sigma^2_0 =17500^2[/tex] represent the value that we want to test
Part a
For this case the claim is:
[tex] \sigma >17500[/tex]
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: [tex]\sigma \leq 17500[/tex]
Alternative hypothesis: [tex]\sigma >17500[/tex]
Calculate the statistic
For this test we can use the following statistic:
[tex]\chi^2 =\frac{n-1}{\sigma^2_0} s^2[/tex]
And this statistic is distributed chi square with n-1 degrees of freedom. We have eveything to replace.
[tex]\chi^2 =\frac{136-1}{17500^2} 18500^2 =150.869[/tex]
