Whole Foods is considering opening two new stores in a city

Whole Foods is considering opening two new stores in a city. Since the prices for their products tends to be higher, they want to know the income levels of the different locations they are considering. The mean annual family income for a sample of 15 people in the first location is $155583, with a standard deviation of $42164. A corresponding sample of 27 people at a secondlocation had a mean of $171497, with a standard deviation of $29840. At the 0.02 significance level, is there a difference in the variability of the incomes between the two locations?

Solution

Null Hypothesis : Mean1 = Mean2

Alternate Hypothesis : Mean1 != Mean2

n1 = 15 , n2 =27

SD1 = 42164 , SD2 = 29840

Mean1 = 155583 , Mean2 = 171497

z = (Mean1 - Mean2)/ sqrt(SD^2/n1 + SD^2/n2)

= ( 155583 - 171497 ) / ((42164)^2/ 15 + (29840^2)/27)

= -0.0001

Alpha = 0.02

From z table since it is two tailed test :

P = 2*(1 - 0.5) = 1

Since P > 0.02

Failed to reject the null hypothesis.