Question

Kroger is in the process of designing a new store to be located in a plaza under development in Mason. They intend to use their Symmes Township store as a model, but they are concerned that the customer base in Mason might have different needs and expectations. One area of concern is in Service Meats. Grocery shoppers in Symmes Township expect a Service Meat counter, and the department has been quite profitable. Kroger would like to know if the expectation of having a Service Meat counter will be the same in Mason as it is in Symmes Township. They survey residents of both areas, and among the questions is, "Do you buy meat from the Service Meat counter on a regular (weekly) basis?" In city a, 505 out of 780 respondents said YES. In city b, 325 out of 620 respondents said YES. Using a = .05, test the claim that the percentage of grocery shoppers who use Service Meats is the same in these two areas of the city.

Answer 1

Given that,
sample one, x1 =505, n1 =780, p1= x1/n1=0.647
sample two, x2 =325, n2 =620, p2= x2/n2=0.524
finding a p^ value for proportion p^=(x1 + x2 ) / (n1+n2)
p^=0.593
q^ Value For Proportion= 1-p^=0.407
null, Ho: p1 = p2
alternate, H1: p1 != p2
level of significance, α = 0.05
from standard normal table, two tailed z α/2 =1.96
since our test is two-tailed
reject Ho, if zo < -1.96 OR if zo > 1.96
we use test statistic (z) = (p1-p2)/√(p^q^(1/n1+1/n2))
zo =(0.647-0.524)/sqrt((0.593*0.407(1/780+1/620))
zo =4.662
| zo | =4.662
critical value
the value of |z α| at los 0.05% is 1.96
we got |zo| =4.662 & | z α | =1.96
make decision
hence value of | zo | > | z α| and here we reject Ho
p-value: two tailed ( double the one tail ) - Ha : ( p != 4.6622 ) = 0
hence value of p0.05 > 0,here we reject Ho
------------------------------------------------------------------------------
null, Ho: p1 = p2
alternate, H1: p1 != p2
test statistic: 4.662
critical value: -1.96 , 1.96
decision: reject Ho
p-value: 0
no evidence to support that the percentage of grocery shoppers who use service meats is the same in these two areas of the city.