5. The length of time between billing dates and checks received and deposited for non-delinquent accounts of an oil company’s monthly credit card customers is 13.5 days with a standard deviation of 3 days. A bank claims if the company used a lockbox system, it could reduce the company’s average time. Thirty-six (36) accounts were randomly selected and tested using the lockbox system. The average time was found to be 13 days. What is your conclusion at the 2.5% level of significance?

Let X be the length of time between billing dates and checks received and deposited for non-delinquent accounts of an oil company’s monthly credit card customers

X has mean 13.5 and sigma 3 days

Sample size = n =36, x bar = 13

[tex]H_0: x bar = 13.5\\H_a: x bar <13.5[/tex]

(One tailed test at 0.025 sign. level)

Mean diff = -0.5

Since sigma is known z test can be used

Std error =[tex]\frac{\sigma}{\sqrt{n} } =0.5[/tex]

Z statistic = -0.5/SE= -0.1

p value = 0.920

p>0.025 hence accept null hypothesis.

My conclusion is there is no statistical evidence that lock box reduced the mean time.