One recent study showed that the average annual amount spent by an East Coast ho

Question

One recent study showed that the average annual amount spent by an East Coast household on
frankfurters was $23.84 compared with an average of $19.83 for West Coast households.
Suppose a random sample of 11 East Coast households showed that the standard deviation of
these purchases (frankfurters) was $7.52, whereas a random sample of 15 West Coast households
resulted in a standard deviation of $6.08. Do these samples provide enough evidence to conclude
that the variance of annual frankfurter purchases for East Coast households is greater than the
variance of annual frankfurter purchases for West Coast households? Let =0.05. Assume
amounts spent per year on frankfurters are normally distributed. Suppose the data did show that
the variance among East Coast households is greater than that among West Coast households.
What might this variance mean to decision makers in the frankfurter industry?

Explanation / Answer

Population mean for the annual amount spent on frankfurters by east coast households 1= sample mean for the given sample size 11

Here standered deviation s1 for frankfurters purchase in 11 east coast households = $7.52

Population mean for the annual amount spent on frankfurters by west coast households 2= sample mean for the given sample size 15

Here standered deviation s2 for frankfurters purchase in 15 west coast households = $6.08

Here We weill do hypotheis testing

Null Hypotheis H0 :  1= 2

Alternative Hypothesis H1 : 1>2 ; it is an upper tailed test.

We shall choose   =0.05 so The hypothesis that the two variances are equal is rejected if

The test statistic is   F=s12/s22= (7.52)2/ (6.08)2 = 1.53

F(0.05/2,11-1,15-1) = F(0.025,10,14) = 2.6022

so Fcritical = 2.6022

F <  Fcritical so we cannot reject the null hypothesis so there is not enough evidence to conclude variance of annual frankfurter purchase for both type of households.

This variance show that there are more variability in eastern households which can impact the frankfurter consumption.

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