Whole Foods is considering opening two new stores in a city. Since the prices fo
ID: 3438252 • Letter: W
Question
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.
Explanation / Answer
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.
---------------------------------------
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.
Group Group One Group Two Mean 155583.00 171497.00 SD 157763.24 152154.74 SEM 42164.00 29840.00 N 14 26Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.