Question

Using the data given in the table below, answer the following questions. (Round your final answers to 3 decimal places.)

    

Order Size and Shipping Cost (n = 12)
Orders (X)	Ship Cost (Y)
1,077	4,489
1,031	5,537
796	3,205
867	4,147
1,139	4,734
1,106	5,496
828	4,428
997	5,591
745	3,321
683	3,527
1,182	6,527
1,038	5,174

  

(a)	Use Excel, MegaStat, or MINITAB to calculate the correlation coefficient.

  

rcalc

   

(b)	Use Excel or Appendix D to find t.025 for a two-tailed test at   α=0.05α=0.05 .

    

    t.025t.025 ±   

    

(c)	Calculate the t test statistic.

    

tcalc

   

(d)	Should we reject the null hypothesis of zero correlation?
	Yes No

Answer 1

The Excel output for regression analysis is:

Simple linear regression results:

Dependent Variable: Ship Cost (Y)
Independent Variable: Orders (X)
Ship Cost (Y) = -302.41019 + 5.2054071 Orders (X)
Sample size: 12
R (correlation coefficient) = 0.84271202
R-sq = 0.71016354
Estimate of error standard deviation: 580.4498

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	-302.41019	1020.6708	≠ 0	10	-0.29628574	0.7731
Slope	5.2054071	1.0516035	≠ 0	10	4.9499713	0.0006

Hence,

a) rcalc = 0.843

b) t0.025 = + 2.228

c) tcalc = 4.950

d) Yes