Respuesta :
Answer:
[tex]\chi^2 =\frac{132-1}{121} 114.49 =123.952[/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=132[/tex] represent the sample size
[tex]\alpha[/tex] represent the confidence level
[tex]s^2 =10.7^2 =114.49 [/tex] represent the sample variance obtained
[tex]\sigma^2_0 =11^2=121[/tex] represent the value that we want to test
Null and alternative hypothesis
On this case we want to check if the population variance specification is violated, so the system of hypothesis would be:
Null Hypothesis: [tex]\sigma^2 \geq 121[/tex]
Alternative hypothesis: [tex]\sigma^2 <121[/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{132-1}{121} 114.49 =123.952[/tex]
Calculate the p value
In order to calculate the p value we need to have in count the degrees of freedom , on this case 131. And since is a right tailed test the p value would be given by:
[tex]p_v =P(\chi^2 <123.952)=0.3438[/tex]
In order to find the p value we can use the following code in excel:
"=1-CHISQ.DIST(123.952,131,TRUE)"
Based on the standard deviation given and the sample size, the test statistic can be found to be 123.95.
What is the value of the test statistic?
The test statistic can be found by the formula:
= ((Sample size - 1) x Standard deviation of sample²) / Standard deviation of population
Solving gives:
= ((132 - 1) x 10.7²) / 11²
= 14,998.19 / 121
= 123.95
In conclusion, the test statistic is 123.95.
Find out more on test statistics at https://brainly.com/question/16628265.
