Question

A company want to find out if there is a linear relationship between indirect labor expense (ILE), in dollars, and direct labor hours (DLH). Data for direct labor hours and indirect labor expense for 25 months are given. Based on the data in the table below, is there a significant linear relationship between Direct Labor Hours and the Indirect Labor Expense?

• A.

  Yes, because the p-value = 0.00023

• B.

  No, the sample correlation coefficient is equal to 0.878, which provides evidence of a significant linear relationship.

• C.

  No, because the p-value = 0.00023

• D.

  Yes, the sample correlation coefficient is equal to 0.878, which provides evidence of a significant linear relationship.

DLH(X)	ILE(Y)
20	361
25	355
22	376
23	384
20	374
19	311
24	427.2
28	387.5
26	450.8
29	475.2
27	462.6
22	333.3
26	389.9
25	445
28	511
32	501.1
33	544.9
35	423.8
34	574.1
30	535.4
36	444.7
37	578.4
37	399.6
31	355
20	313

Answer 1

We need to find the sums ∑x , ∑y, ∑x*y, ∑x2 and ∑y2

∑x =699 , ∑y =10713.5, ∑x*y = 302477.1, ∑x2 = 19763 and ∑y2 =4739569

r =

r =

r = 0.6729

Test statistic t =

=

t = 4.36

P value : We can use excel function =TDIST( |t| ,df , tail ) to find the P value

| t | is positive value of test statistic t, df = n-2 = 25-2 = 23  and tail =1 for one tail and 2 for two tail

=TDIST(4.3,23,2 )

=0.00023

As P value is less than 0.05 ,there a significant linear relationship between Direct Labor Hours and the Indirect Labor Expense

Answer : A) Yes, because the p-value = 0.00023