Download Section 9.5

Section 9.5 Hypothesis Test for One Population Mean When
 is unknown
When  is unknown the sample standard deviation is used.
Instead of the one mean z-test, the one mean t-test or more
simply known as the t-test is used. The studentized version of
is
t
x
x  0
s
n
Also it will be important to estimate the p-value of the test for our
three different alternative hypotheses
P-value
t0
Right tailed Test
Z0
P-value
P-value
 t0
t0
Two tailed Test
t0
Left tailed Test
In all three cases if the P  value   ,then the null hypothesis is
rejected.
Example
Examples
9.106
Active management of labor (AML) is a group of interventions
designed to help reduce the length of labor and the rate of
cesarean deliveries. Physicians were interested in determining
whether AML would translate into a reduced cost for delivery.
According to the article published on this study, 200 AML
deliveries had a mean cost of $2480 with a standard deviation of
$776. At the time of the study, the average cost of having a baby
in a U.S. hospital was $2528. At the 5% significance level, do the
data provide sufficient evidence to conclude that, on average,
AML reduces the cost of having a baby in a U.S. hospital?
9.104
According to the document Consumer Expenditures, a publication
of the Bureau of Labor Statistics, the average consumer unit
spent $1874 on apparel and services in 2006. The same year, 25
consumer units in the Northeast had the following annual
expenditures, in dollars, on apparel and services. At the 5%
significance level, do the data provide sufficient evidence to
conclude that the 2006 mean annual expenditure on apparel and
services for consumer units in the Northeast differed from the
national mean of $1874. The sample mean and sample standard
deviation of the data are $2060.76 and $350.90.