A local bank claims that the waiting time for its customers to be served is the

Question

A local bank claims that the waiting time for its customers to be served is the lowest in the area. A competitor bank checks the waiting times at both banks. The sample statistics are listed below. Test the local bank’s claim. Use the information given below. State the null and alternative hypotheses, the significance level, the critical value, the test statistic, the decision and conclusion.



Local Bank Competitor Bank

Sample size n1 = 45 n2 = 50



Average Waiting x1= 2.3 min. x2= 2.6 min.

time in minutes

for each sample



Sample standard s1 = 1.1 min. s 2 = 1.0 min.

Deviation of each

Explanation / Answer

The test hypothesis is

Ho: local mean - competitor mean = 0
Ha: local mean - competitor mean < 0

test statistic:

t =(xbar1 -xbar2) /[s1^2/n1 + s2^2/n2]

=(2.3-2.6)/sqrt(1.1^2/45 + 1^2/50)
=-1.385

If a=0.05, the critical value is t(0.025, df=n1+n2-2=45+50-2=93) =-1.99 (check student t table)

Since t=-1.385 > -1.99, we do not reject Ho.

So we can conclude that the waiting times are the same.

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