Showton Middle School has 840 students. Teresa surveys a random sample of 60 students and finds that 8 of them have more than 3
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Answer:
And we can use the following excel code to find the p value:"=2*(1-F.DIST(5.286,25,24,TRUE))"
Since the we have enough evidence to reject the null hypothesis. And we can say that we have enough evidence to conclude that we have significant differences between the two variances at 5% of significance.
Step-by-step explanation:
Data given and notation
represent the sampe size for seniors
represent the sample size for managers
represent the sample variance for seniors
represent the sample variance for managers
represent the significance level provided
Confidence =0.95 or 95%
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:
Solution to the problem
System of hypothesis
We want to test if we have a significant difference between the variances of salaries for seniors and managers, so the system of hypothesis are:
H0:
H1:
Calculate the statistic
Now we can calculate the statistic like this:
Now we can calculate the p value but first we need to calculate the degrees of freedom for the statistic. For the numerator we have and for the denominator we have
and the F statistic have 25 degrees of freedom for the numerator and 24 for the denominator. And the P value is given by:
P value
And we can use the following excel code to find the p value:"=2*(1-F.DIST(5.286,25,24,TRUE))"
Conclusion
Since the we have enough evidence to reject the null hypothesis. And we can say that we have enough evidence to conclude that we have significant differences between the two variances at 5% of significance.