Respuesta :
Answer:
b. 2.70
Step-by-step explanation:
Data given and notation
[tex]n_1 = 11 [/tex] represent the sampe size for sample 1
[tex]n_2 =8[/tex] represent the sample size for sample 2
[tex]s_1 [/tex] represent the sample deviation for sample 1
[tex]s^2_1 [/tex] represent the sample variance for sample 1
[tex]s_2[/tex] represent the sample deviation for sample 2
[tex]s^2_2 [/tex] represent the sample variance for sample 2
[tex]\alpha=0.1[/tex] represent the significance level provided
Confidence =0.90 or 90%
F test is a statistical test that uses a F Statistic to compare two population variances, with the sample deviations s1 and s2. The F statistic is always positive number since the variance it's always higher than 0. The statistic is given by:
[tex]F=\frac{s^2_1}{s^2_2}[/tex]
System of hypothesis
We want to test for example if the variation for group 1 it's higher than the variation for group 2, so the system of hypothesis are:
H0: [tex] \sigma^2_1 \leq \sigma^2_2[/tex]
H1: [tex] \sigma^2_1 >\sigma^2_2[/tex]
Calculate the statistic
Now we can calculate the statistic like this:
[tex]F=\frac{s^2_1}{s^2_2}=F_{calc}[/tex]
Calculate the critical value
Now we can calculate the critical value but first we need to calculate the degrees of freedom for the statistic. For the numerator we have [tex]n_1 -1 =11-1=10[/tex] and for the denominator we have [tex]n_2 -1 =8-1=7[/tex] and the F statistic have 10 degrees of freedom for the numerator and 7 for the denominator. And the critical value would be:
[tex]F_{crit}=2.705[/tex]
And we can find it with the following excel code: "=F.INV(0.9,10,7)"
b. 2.70
