Suppose that a health plan asserts that a patient hospitaliz

Suppose that a health plan asserts
that a patient hospitalized with
coronary heart disease requires
no more than 6.5 days of hospital
care. However, we believe that a
stay of 6.5 days is too low. To examine
the claim of the health
plan, assume further that we collected
data depicting the lengths
of stay of 40 patients who were
hospitalized recently with coronary
heart disease. The results of
the sample are as follows:
5, 8, 9, 12, 7, 9, 10, 11, 4, 7, 8, 5, 8,
13, 11, 10, 6, 5, 8, 9,
5, 12, 7, 9, 4, 8, 7, 7, 11, 5, 8, 10, 5,
8, 2, 11, 3, 6, 8, 7

If 0.05, use these data to
evaluate the claim by the health
plan.

Solution

sample mean=7.7

sample standard deviatoin = 2.613574

Let mu be the population mean

The test hypothesis:

Ho: mu = 6.5 (i.e. null hypothesis)

Ha: mu>6.5 (i.e. alternative hypothesis)

The test statistic is

Z=(xbar-mu)/(s/vn)

=(7.7-6.5)/(2.613574/sqrt(40))

=2.90

It is a right-tailed test.

Given a=0.05, the critical value is Z(0.05) = 1.645 (from standard normal table)

Since Z=2.90 is larger than 1.645, we reject the null hypothesis.

So we can conclude that a stay of 6.5 days is too low.