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.