A company is evaluating a new training method to reduce costs administrative. the company tests, he tests the new method to compare it with the existing method in the company. Two groups of employees are formed, the first with 7 administrative employees testing the new method, and the second with 10 employees working with the existing method. The decrease in costs mean of each group, as well as the sample standard deviation of the same costs are reported below:

Lower costs New method:

n1 = 7 X= 3260 s₁ = 210

Existing Method:

n2 = 10 Y = 3240 S₂ = 190

a) (10 pts) Calculate a 95% confidence interval for the difference in the means of cost reduction using the different training methods.

b) (10 pts) Do these data provide sufficient evidence to say that the method New is better because it lowers average administrative costs more? Perform a hypothesis test with the 5% significance level. Do not forget specify the hypotheses, test statistic, and conclusion of your test.

c) (2.5 pts) What is the P-value of the test? Mark on your graph.

d) (10 pts) Do these data provide sufficient evidence to say that the variance in Is the decrease in administrative costs different for the two methods? Makes a hypothesis test with the 5% significance level. Don't forget to specify the hypotheses, the test statistic, and the conclusion of your test.

e) (2.5 pts) What is the P-value of the test?Mark on your graph.