Answer:
Since the we have enough evidence to FAIL to reject the null hypothesis. And we can say that we don't have enough evidence to conclude that the variation for the New sample it's significantly less than the variation for the Old sample at 5% of significance.
Step-by-step explanation:
Data given and notation
represent the sampe size for the Old
represent the sample size for the New
represent the sample mean for Old
represent the sample mean for the New
represent the sample deviation for Old
represent the sample deviation for New
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 the variation for New sample it's lower than the variation for the Old sample, 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 15 degrees of freedom for the numerator and 10 for the denominator. And the P value is given by:
P value
Since we have a left tailed test the p value is given by:
And we can use the following excel code to find the p value:"=F.DIST(0.64,15,10,TRUE)"
Conclusion
Since the we have enough evidence to FAIL to reject the null hypothesis. And we can say that we don't have enough evidence to conclude that the variation for the New sample it's significantly less than the variation for the Old sample at 5% of significance.