Respuesta :
Answer:
For this problem we are assuming that the confidence level is 99% or 0.99, then the significance level would be [tex]\alpha=0.01[/tex] then the value of [tex]\alpha/2 =0.005[/tex] and the degrees of freddom are given by:
[tex] df =n-1 = 19-1=18[/tex]
Then the critical values for this case are:
[tex]\chi^2_{\alpha/2}=6.265[/tex]
[tex]\chi^2_{1-\alpha/2}=37.156 [/tex]
Step-by-step explanation:
For this problem we are assuming that the confidence level is 99% or 0.99, then the significance level would be [tex]\alpha=0.01[/tex] then the value of [tex]\alpha/2 =0.005[/tex] and the degrees of freddom are given by:
[tex] df =n-1 = 19-1=18[/tex]
Then the critical values for this case are:
[tex]\chi^2_{\alpha/2}=6.265[/tex]
[tex]\chi^2_{1- \alpha/2}=37.156 [/tex]
Using a calculator for the chi-square distribution, it is found that the critical values are [tex]\chi^2_r = 6.2648[/tex] and [tex]\chi^2_r = 37.1565[/tex].
For a chi-square critical value, three parameters are needed:
- The number of degrees of freedom, which is one less than the sample size.
- The confidence level.
- Whether the test is one-tailed or two-tailed.
In this problem:
- Sample size of 19, hence 18 df.
- 99% confidence level, and two-tailed.
Hence, using a calculator, the critical values are [tex]\chi^2_r = 6.2648[/tex] and [tex]\chi^2_r = 37.1565[/tex].
A similar problem is given at https://brainly.com/question/13780944
