Question

A study was to be designed to determine whether food prices charged in the inner city are higher then the prices charged in suburban areas. A market basket of goods was comprised, with the total cost of the goods obtained at n inner city stores and n suburban stores.Assume that cost of the goods has a normal distribution with a range of $115 to $135 for the inner city stores and $100 to $120 for the suburban stores. Determine the sample size needed so that we would be 95% confident that the estimated difference in the mean costs is within $4 of the true difference.

Answer 1

Assume that cost of the goods has a normal distribution with a range of $115 to $135 for the inner city stores and $100 to $120 for the suburban stores.

Range for the inner city stote = 135 - 115 = 20

Standard deviation for the inner city stores is,

range / 4 = 20 / 4 = 5 that is, sd1 = $5

Rane for suburban store = 120 - 100 = 20

standard deviation for the suburban store is,

range / 4 = 20 / 4= 5 that is, sd2 = $5

Margin of error ( E ) = $4

A 95% confidnce level has significance level = 0.05 and has critical value is,

We want to find, the sample size ( n = n1 = n2)

Therefore, required sample size is 12