Question

Bardi Trucking Co., located in Cleveland, Ohio, makes deliveries in the Great Lakes region, the Southeast, and the Northeast. Jim Bardi, the president, is studying the relationship between the distance a shipment must travel and the length of time, in days, it takes the shipment to arrive at its destination. To investigate, Mr. Bardi selected a random sample of 20 shipments made last month. Shipping distance is the independent variable and shipping time is the dependent variable. The results are as follows:

Shipment		Distance (miles)	Shipping Time (days)		Shipment	Distance (miles)	Shipping Time (days)
1		702	13		11	716	5
2		634	13		12	688	10
3		710	5		13	677	14
4		829	15		14	795	7
5		635	7		15	709	3
6		643	7		16	702	12
7		851	8		17	798	7
8		853	5		18	690	6
9		727	6		19	632	7
10		716	5		20	650	12

. Fill in the blanks. (Round your answers to 3 decimal places. Negative values should be indicated by minus sign.)

x¯x¯
y¯y¯
Sx
Sy
r

b-2. State the decision rule for 0.10 significance level: H₀: ρ ≤ 0; H₁: ρ > 0. (Round your answer to 3 decimal places.)

b-3. Compute the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 3 decimal places.)

b-4. Can we conclude that there is a positive correlation between distance and time? Use the 0.10 significance level.

c-1. Determine the coefficient of determination. (Round your answer to 3 decimal places.)

c-2. Fill in the blank below. (Round your answer to 1 decimal places.)

? % of the variation in shipping time is explained by shipping distance.​

Determine the standard error of estimate. (Round your answer to 3 decimal places.)

Answer 1

(a)

	717.85
	8.35
Sx	71.18
Sy	3.573
r	-0.117

b-1)  the decision rule for 0.10 significance level: H0: ρ ≤ 0; H1: ρ > 0 is

reject H0 if t>tc=1.33

b-2) The test statistic is

  

b-3) Since t=-0.4998 < tc=1.33, do not reject H0.

   we cant conclude that there is a positive correlation between distance and time at 0.10 significance level.

c-1) the coefficient of determination is

  

c-2) 1.4 % of the variation in shipping time is explained by shipping distance.​

The standard error of estimate is 3.646.