Answer:
The null hypothesis is [tex]H_o : \sigma^2_1 = \sigma^2 _2[/tex]
The alternative hypothesis is [tex]H_a : \sigma^2_1 \ne \sigma^2 _2[/tex]
The conclusion is
There is no sufficient evidence to conclude that there is a difference between the variances of salaries for seniors and managers
Step-by-step explanation:
From the question we are told that
The variance for seniors is [tex]s ^2_1 = 2.3[/tex]
The variance for managers is [tex]s ^2_2 = 11.3[/tex]
The first sample size is [tex]n_1 = 25[/tex]
The second sample size is [tex]n_2 = 26[/tex]
The significance level is [tex]\alpha = 0.05[/tex]
The null hypothesis is [tex]H_o : \sigma^2_1 = \sigma^2 _2[/tex]
The alternative hypothesis is [tex]H_a : \sigma^2_1 \ne \sigma^2 _2[/tex]
Generally the test statistics is mathematically represented as
[tex]F = \frac{s_1^2}{s_2^2}[/tex]
=> [tex]F = \frac{2.3}{11.3}[/tex]
=> [tex]F = \frac{2.3}{11.3}[/tex]
=> [tex]F = 0.2035[/tex]
Generally the p-value is obtain for the F-distribution table (Reference - Free statistic calculator ) at a degrees of freedom
[tex]df_1 = 25 - 1[/tex]
[tex]df_1 = 24[/tex]
and [tex]df_2 = 26 - 1[/tex]
[tex]df_2 = 25[/tex]
The p- value is
[tex]p-value = f_{0.2035,24,25} = 0.99989[/tex]
So from the calculation we see that
[tex]p-value > \alpha[/tex]
So we fail to reject the null hypothesis
