Question

Frank Furter, owner of Frank’s Fast Food, is concerned about the wait time for customers at his restaurant. He serves breakfast from 6:30 until 10:30, then the regular menu for the rest of the day. Frank assumes the distribution of wait times is normal and while the average wait times between breakfast and lunch customers are similar, Frank is concerned that the regular menu (served during the lunch time) causes more variability in the wait times. Frank had a consultant take samples and calculate the variance for wait times for breakfast and lunch customers. The consultant randomly sampled 40 breakfast wait times and 36 lunch wait times with the following results: Breakfast s2 = 3.1 Lunch s2 = 5.2 Use the six-step hypothesis testing process. At the 0.05 significance level, is there evidence that there is more variability in the lunch wait times than breakfast wait times? Do your work in Excel please

Answer 1

null hypothesis:		σ21	=		σ22
Alternate Hypothesis:		σ21	<		σ22

n1                  =		40
n2                  =		36
degree of freedom of numerator v1      =		39
degree of freedom of denominator v2 =		35
s12	=	3.1000
s22	=	5.2000

for 5 % level and given df critical values of F      =					0.580
Decision rule:reject Ho if test statistic F in critical region:			F	<	0.580

test stat F: =

s12/s22

=

0.596

as test statistic is not in critical region ; we can not reject null hypothesis

we do not have sufficient evidence to conclude that there is more variability in the lunch wait times than breakfast wait times