Question

A service counter manager wishes to ensure that an average of 16 seconds to serve a customer. In order to analyse the efficiency of the service process, he takes a random sample of 56 customers. The mean service time of the sample is 15.8 seconds. Assume that the population standard deviation is 0.8 seconds.

(i)    State the null and the alternative hypotheses for the test.    [2 marks]
(ii)   Test the manager's concern at α=0.05. [6 marks]

(iii)   What recommendation can the manager present to the company?      [2 marks]

Answer 1

a)

H0: = 16

Ha: 16

b)

Test statistics

z = ( - ) / ( / sqrt(n) )

= ( 15.8 - 16) / (0.8 / sqrt(56 ) )

= -1.87

Critical values at 0.05 level = -1.96 , 1.96 .

Since | z | < 1.96 , Fail to reject H0.

c)

We conclude that an average to serve customer is 16 seconds and the service process is efficient.