HOW TO SELL A BURGER A fastfood chain wants to compare two w

HOW TO SELL A BURGER. A fast-food chain wants to compare two ways of promoting a new burger ( turkey burger). One way uses a coupon available at the store. Before the promotion, their marketing research group matches 50 pairs of stores. Each pair has two stores with similar sales volume and customer demographics. The store in a pair that uses coupons is randomly chosen, and after a month long promotion, the increases in sales of the turkey burger are compared for the two stores. THe increase was gigher for 28 stores using coupons and higher for 22 stores using the poster. Is this strong evidence to support the coupon approach, or could this outcome be explained by chance? Answer by performing all five steps of a two-sided significance test about the population proportion of times the sales would be higher with the coupon promotion. *number and clearly display all eight steps of hypothesis testing.

Solution

Null Hypothesis, There Is No Significance between them Ho: p1 = p2
Alternate, proportion of times the sales would be higher with the coupon promotion H1: p1 > p2
Test Statistic
Sample 1 : X1 =28, n1 =50, P1= X1/n1=0.56
Sample 2 : X2 =22, n2 =50, P2= X2/n2=0.44
Finding a P^ value For Proportion P^=(X1 + X2 ) / (n1+n2)
P^=0.5
Q^ Value For Proportion= 1-P^=0.5
we use Test Statistic (Z) = (P1-P2)/(P^Q^(1/n1+1/n2))
Zo =(0.56-0.44)/Sqrt((0.5*0.5(1/50+1/50))
Zo =1.2
| Zo | =1.2
Critical Value
The Value of |Z | at LOS 0.05% is 1.645
We got |Zo| =1.2 & | Z | =1.645
Make Decision
Hence Value of |Zo | < | Z | and Here we Do not Reject Ho
P-Value: Right Tail -Ha : ( P > 1.2 ) = 0.11507
Hence Value of P0.05 < 0.11507,Here We Do not Reject Ho