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.

a. At the 0.02 significance level, is there a difference in the variability of the incomes between the two locations?  Show work as stated in the quiz directions.

b. Given the result from part (a) on variances, test whether there is a difference in the average income between the two locations. Use a 0.01 significance level. (If you need it, the ugly degrees of freedom are 49.) Show work as stated in the quiz directions.

Solution

a) Alpha = 0.02

H0: Var 1 = Var 2

Ha: Var 1 not equal to var 2

Two tailed test for variances.

F statistic = s1^2/s2^2 = 1.997

df = 14, 26

p value =0.0616

As p > 0.02, accept null hypothesis.

There is statistical evidence to conclude that variances are equal.

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H0: mu1 = mu2

Ha: mu1 not equal to mu2

Two tailed test at 1% level for equal variances.

t = 0.3081
  df = 25
  standard error of difference = 51654.898

The two-tailed P value equals 0.7606
  By conventional criteria, this difference is considered to be not statistically significant.

Hence we can take as means are equal for two groups.