Respuesta :
Answer:
[tex] t=(26-1) [\frac{0.18}{0.25}]^2 =12.96[/tex]
What is the critical value for the test statistic at an α = 0.01 significance level?
Since is a two tailed test the critical zone have two zones. On this case we need a quantile on the chi square distribution with 25 degrees of freedom that accumulates 0.005 of the area on the left tail and 0.995 on the right tail. Â
We can calculate the critical value in excel with the following code: "=CHISQ.INV(0.005,25)". And our critical value would be [tex]\Chi^2 =10.520[/tex] Â Â
And the right critical value would be : Â [tex]\Chi^2 =46.927[/tex]
And the rejection zone would be: [tex] \chi^2 < 10.52 \cup \chi^2 >46.927[/tex]
Since our calculated value is NOT in the rejection zone we FAIL to reject the null hypothesis.
Step-by-step explanation:
Previous concepts and notation
The chi-square test is used to check if the standard deviation of a population is equal to a specified value. We can conduct the test "two-sided test or a one-sided test".
n = 26 sample size
s= 0.18
[tex]\sigma_o =0.25[/tex] the value that we want to test
[tex]p_v [/tex] represent the p value for the test
t represent the statistic
[tex]\alpha=0.01[/tex] significance level
State the null and alternative hypothesis
On this case we want to check if the population standard deviation is equal to 0.25, so the system of hypothesis are:
H0: [tex]\sigma =0.25[/tex]
H1: [tex]\sigma \neq 0.25[/tex]
In order to check the hypothesis we need to calculate the statistic given by the following formula:
[tex] t=(n-1) [\frac{s}{\sigma_o}]^2 [/tex]
This statistic have a Chi Square distribution distribution with n-1 degrees of freedom.
What is the value of your test statistic?
Now we have everything to replace into the formula for the statistic and we got:
[tex] t=(26-1) [\frac{0.18}{0.25}]^2 =12.96[/tex]
What is the critical value for the test statistic at an α = 0.01 significance level?
Since is a two tailed test the critical zone have two zones. On this case we need a quantile on the chi square distribution with 25 degrees of freedom that accumulates 0.005 of the area on the left tail and 0.995 on the right tail. Â
We can calculate the critical value in excel with the following code: "=CHISQ.INV(0.005,25)". And our critical value would be [tex]\Chi^2 =10.520[/tex]
And the right critical value would be : Â [tex]\Chi^2 =46.927[/tex]
And the rejection zone would be: [tex] \chi^2 < 10.52 \cup \chi^2 >46.927[/tex]
Since our calculated value is NOT in the rejection zone we FAIL to reject the null hypothesis.
