Question

7. Suppose Burger King has run a major ad campaign with the aim of increasingly monthly sales. To investigate the effectiveness of this campaign, BK randomly selected 7 restaurants and recorded the monthly sales before and after the ad campaign. They found that the standard deviation of the difference in the after and before data was $10.41. Let before campaign be population 1 and after campaign be population 2. 1 2 3 3 4 5 6 Restaurant After (in $1,000 Before (in $1,000) $127 $122 $145 $156 $160 $134 $108 $107 $110 $143 $168 $145 $125 $98 a. Set up the null and alternative hypotheses to test if the ad campaign was effective. b. Compute an appropriate test statistic. c. Conclude at a = 0.05. Explain.

Answer 1

a) let μ_d =μ₂-μ₁

null Hypothesis:		μd	=	0
alternate Hypothesis:		μd	>	0

b)

S. No	after	before	difference(d)=x1-x2
1	127	107	20
2	122	110	12
3	145	143	2
4	156	168	-12
5	160	145	15
6	134	125	9
7	108	98	10
	total	=	Σd=56
	mean dbar=	d̅                           =	8.0000

test statistic t =(dbar)*sqrt(n)/standard deviation =8*sqrt(7)/10.41 =2.034

c)

for 0.05 level with right tailed test and n-1= 6 degree of freedom, critical value of t=

1.943

as test statistic falls in rejection region, we reject the null hypothesis and conclude that ad campaign was effective,