Question

3. A local bank claims that the standard deviation of waiting time for its customers to be served is lower than its competitors. A sample of 15 waiting times at the local bank had a standard deviation of 1.1 minutes. A sample of 16 waiting times from the competing bank had a standard deviation of 1.3 minutes. Does the data support the local bank’s claim?

Answer 1

let σ₁  and σ₂ are population standard deviation of local and competitor bank

Null Hypothesis: Ho σ1	=	σ2
Alternate hypothesis: Ha        σ2	<	σ2

	n1    =	15
	n2    =	16
df of numerator v1 =n1-1=		14
df of denominator v2=n2-1 =		15

for 5 % level left tailed test and given df critical values of F      =0.41
Decision rule:reject Ho if test statistic F in critical region: F<0.41

Test statistic =s12/s22 =(1.1/1.3)^2 =

0.72

since test statistic is not less than critical value , we can not reject null hypothesis

we do not have sufficient evidence at 0.05 level to conclude that  waiting time for local bank customers to be served is lower than its competitors.