Respuesta :
Answer:
[tex]\chi^2 =\frac{10-1}{18} 23.04 =11.52[/tex]
The degrees of freedom are:
[tex] df =n-1=10-1=9[/tex]
Now we can calculate the critical value taking in count the alternative hypotheis we have two values:
[tex]\chi^2_{\alpha/2}= 2.70[/tex]
[tex]\chi^2_{1-\alpha/2}= 19.02[/tex]
Since the calculated value is between the two critical values we FAIL to reject the null hypothesis and we can't conclude that the true variance is different from 18
Step-by-step explanation:
Information given
[tex]n=10[/tex] represent the sample size
[tex]\alpha=0.05[/tex] represent the confidence level
[tex]s^2 =4.8^2= 23.04 [/tex] represent the sample variance obtained
[tex]\sigma^2_0 =18[/tex] represent the value to verify
System of hypothesis
We want to verify if the true variance is different from 18, so the system of hypothesis would be:
Null Hypothesis: [tex]\sigma^2 = 18[/tex]
Alternative hypothesis: [tex]\sigma^2 \neq 18[/tex]
The statistic would be given by:
[tex]\chi^2 =\frac{n-1}{\sigma^2_0} s^2[/tex]
And replacing we got:
[tex]\chi^2 =\frac{10-1}{18} 23.04 =11.52[/tex]
The degrees of freedom are:
[tex] df =n-1=10-1=9[/tex]
Now we can calculate the critical value taking in count the alternative hypotheis we have two values:
[tex]\chi^2_{\alpha/2}= 2.70[/tex]
[tex]\chi^2_{1-\alpha/2}= 19.02[/tex]
Since the calculated value is between the two critical values we FAIL to reject the null hypothesis and we can't conclude that the true variance is different from 18
