Chapter 9: Introduction to Hypothesis Testing

392 CHAPTER 9 • INTRODUCTION TO HYPOTHESIS TESTING
where:
x Sample mean
Hypothesized value for the population mean
s Sample standard deviation,
n Sample size
s
∑( xx) 2
n1
In order to employ the t-distribution, we must make the following assumption:
Assumption
The population is normally distributed.
If the population from which the simple random sample is selected is approximately
normal, the t-test statistic computed using Equation 9.3 will be distributed according to a
t-distribution with n 1 degrees of freedom.
SUMMARY One- or Two-Tailed Tests for , Unknown
1. Specify the population parameter of interest, μ.
2. Formulate the null hypothesis and the alternative
hypothesis.
3. Specify the desired significance level (α).
4. Construct the rejection region.
If it is a two-tailed test, determine the critical values
for each tail, t /2
and t /2
, from the t-distribution table. If
the test is a one-tailed test, find either t
or t
, depending
on the tail of the rejection region. Degrees of freedom
are n 1. If desired, the critical t-values can be used to
find the appropriate x or the /2L and /2U Values.
x x
Define the decision rule.
a. If the test statistic falls into the rejection region,
reject H 0
; otherwise, do not reject H 0
.
b. If the p-value is less than α, reject H 0
; otherwise, do
not reject H 0
.
5. Assuming that the population is approximately normal,
compute the test statistic.
Select the random sample and calculate the sample
mean, x ∑ x/
n, and the sample standard deviation,
∑( x x) s
2
. Then calculate
n1
6. Reach a decision.
7. Draw a conclusion.
x
t
or p-value
s
n
EXAMPLE 9-7 Hypothesis Test for , Unknown
TRY PROBLEM 9.15
Dairy Fresh Ice Cream The Dairy Fresh Ice Cream plant in Greensboro,
Alabama, uses a filling machine for its 64-ounce cartons. There is some variation in the
actual amount of ice cream that goes into the carton. The machine can go out of adjustment
and put a mean amount either less or more than 64 ounces in the cartons. To monitor
the filling process, the production manager selects a simple random sample of 16
filled ice cream cartons each day. He can test whether the machine is still in adjustment
using the following steps:
Step 1 Specify the population parameter of interest.
The manager is interested in the mean amount of ice cream.