Question

The CVS Pharmacy located on US 17 in Murrells Inlet has been one of the busiest pharmaceutical retail stores in South Carolina for many years. To try and capture more business in the area, CVS top management opened another store about 6 miles west on SC 707. After a few months, CVS management decided to compare the business volume at the two stores. One way to measure business volume is to count the number of cars in the store parking lots on random days and times. The results of the survey from the last 3 months of the year are reported below. To explain, the first observation was on October 2 at 20:52 military time (8:52 p.m.). At that time there were four cars in the US 17 lot and nine cars in the SC 707 lot. At the 0.05 significance level, is it reasonable to conclude that, based on vehicle counts, the US 17 store has more business volume than the SC 707 store?

			Vehicles Count
Date	Time		US 17		SC 707
Oct 2	20:52		4		9
Oct 11	19:30		5		7
Oct 15	22:08		9		12
Oct 19	11:42		4		5
Oct 25	15:32		10		8
Oct 26	11:02		9		15
Nov 3	11:22		13		7
Nov 5	19:09		20		3
Nov 8	15:10		15		14
Nov 9	13:18		15		11
Nov 15	22:38		13		11
Nov 17	18:46		16		12
Nov 21	15:44		17		8
Nov 22	15.34		15		3
Nov 27	21:42		20		6
Nov 29	9:57		17		13
Nov 30	17:58		5		9
Dec 3	19:54		7		13
Dec 15	18:20		11		6
Dec 16	18:25		14		15
Dec 17	11:08		8		8
Dec 22	21:20		10		3
Dec 24	15:21		4		6
Dec 25	20:21		7		9
Dec 30	14:25		19		4

1. State the decision rule: H₀: μ _{US 17} − μ _{SC 707} = μ_d ≤ 0  H₁: μ_d > 0. (Round your answer to 3 decimal places.) Reject H0 if t >:

2. Compute the value of the test statistic. (Round your answer to 3 decimal places.)

3. What is your decision regarding H₀?

• Reject H₀

• Do not reject H₀

Answer 1

SAMPLE 1	SAMPLE 2	difference , Di =sample1-sample2	(Di - Dbar)²
4	9	-5	60.840
5	7	-2	23.040
9	12	-3	33.640
4	5	-1	14.440
10	8	2	0.640
9	15	-6	77.440
13	7	6	10.240
20	3	17	201.640
15	14	1	3.240
15	11	4	1.440
13	11	2.000	0.640
16	12	4.000	1.440
17	8	9.000	38.440
15	3	12.000	84.640
20	6	14.000	125.440
17	13	4.000	1.440
5	9	-4.000	46.240
7	13	-6.000	77.440
11	6	5.000	4.840
14	15	-1.000	14.440
8	8	0.000	7.840
10	3	7.000	17.640
4	6	-2.000	23.040
7	9	-2.000	23.040
19	4	15.000	148.840

Ho :   µd=   0
Ha :   µd >   0

a)

Degree of freedom, DF=   n - 1 =    24  
t-critical value , t* =        1.7109   [excel function: =t.inv(α,df) ]

decison rule: reject Ho if t > 1.7109

b)

mean of difference ,    D̅ =ΣDi / n =   2.800                  
                          
std dev of difference , Sd =    √ [ (Di-Dbar)²/(n-1) =    6.589                  
                          
std error , SE = Sd / √n =    6.5891   / √   25   =   1.3178      
                          
t-statistic = (D̅ - µd)/SE = (   2.8   -   0   ) /    1.3178   =   2.125 (answer)

c)

Decison: reject Ho (because test stat = 2.15 > 1.7109 )