Apparently, the smaller is μT value (namely the shorter is
the average housekeeping time), the better is the hotel’s
business performance; or, the smaller is σT value, the
smaller is the difference of housekeeping time, and at this
time relatively, the index value is bigger. Hence, it’s
obvious that the index CI can respond to the situation of
housekeeping time reasonably. Because all parameters
of cleaning and tidying are unknown, the evaluation value
of the index can be obtained by samples. Meanwhile,
because sampling has errors, it’s not objective to judge
whether the housekeeping time reaches an enterprise’s
demand with the index evaluation value merely.
Therefore, the statistical test is one of the objective
methods to evaluate the housekeeping time. The test
hypothesis can be shown as follows: