Question

5. One of the main measures of quality of service provided by any business organization is the speed with which it responds to customer complaints. A medium family held department store, selling furniture and flooring, has been historically resolving customer complaints in 20 days on average, starting from the date the complaint was received. In an effort to improve their performance, however, they have hired an additional expert on customer care. The management is trying to evaluate the effectiveness of the new employee in improving the speed with which customer complaints are addressed. For this purpose, data were obtained for 30 randomly selected customer complaints submitted after the new expert was hired last year. The sample results show that the complaints took an average time of 18.5 days to resolve. The population standard deviation for the time it takes to resolve the customer complaints is 4 days. Based on the given evidence and at 5% level of significance please test whether the performance of the company has improved in resolving customer complaints. Does your conclusion change if you redo the test at 1% level of significance? Show all the necessary steps and explain your conclusion for each test. .

Answer 1

Solution :

= 20

= 18.5

= 4

n = 30

This is the two tailed test .

The null and alternative hypothesis is

H₀ :   = 20

H_a : 20

Test statistic = z

= ( - ) / / n

= (18.5 - 20) / 4 / 30

= -2.05

P (Z < -2.05) = 0.04

P-value = 0.04

= 0.05  

0.04 < 0.05

Reject the null hypothesis .

There is sufficient evidence to suggest that   

= 0.01

0.04≥0.01

Fail to reject the null hypothesis

There is insufficient evidence to suggest that