Question

A mail-order business prides itself in its ability to fill customers' orders in six calendar days...

A mail-order business prides itself in its ability to fill customers' orders in six calendar days or less on the average. Periodically, the operations manager selects a random sample of customer orders and determines the number of days required to fill the orders. Based on this sample information, he decides if the desired standard is not being met. He will assume that the average number of days to fill customers' orders is six or less unless the data suggest strongly otherwise. On one occasion where a sample of 50 customers was selected, the average number of days was 6.75, with a sample standard deviation of 1.5 days. Can the operations manager conclude that his mail-order business is achieving its goal? Use a significance level of 0.05 to answer this question.

Homework Answers

Answer #1
null hypothesis: HO: μ = 6
Alternate Hypothesis: Ha: μ > 6
0.05 level with right tail test and n-1= 49 df, critical t= 1.677 from excel: t.inv(0.95,49)
Decision rule :reject Ho if test statistic t>1.677
population mean μ= 6
sample mean 'x̄= 6.750
sample size    n= 50
std deviation s= 1.500
std error ='sx=s/√n=1.5/√50= 0.2121
t statistic ='(x̄-μ)/sx=(6.75-6)/0.212= 3.536
since test statistic falls in rejection region we reject null hypothesis

we have sufficient evidence to conclude that his mail-order business is not achieving its goal.

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