9.6 - Hypothesis Tests for one Population Mean when  is
unknown
 We’ll use a t-distribution instead of the standard normal distribution
 We’ll use table IV to obtain the critical values
 Table IV can be also used to estimate the p-values. Instead we’ll use a
calculator to find the p-values.
The One-Sample t-Test for a Population Mean
(Critical Value approach)
Assumptions
1. Normal population or large sample
2.  unknown
Step 1. The null hypothesis is  = o and the alternative hypothesis is
Ha: o
or Ha: o or Ha: o
(two-tailed)
(left-tailed)
(right-tailed)
Step 2. Decide on the significance level, .
Step 3. The critical values are
t/2
or
(two-tailed)
-t
or
(left-tailed)
+t
(right-tailed)
Use table IV to find the critical value(s). with df = n - 1
*** see graphs page 436
Step 4. Compute the value of the test statistic
t
x  o
s
n
Step 5. If the value of the test statistic falls in the rejection region, reject Ho;
otherwise, do not reject Ho.
Step 6. Interpret the results of the hypothesis test.
*** see example 9.17, p. 438 (critical value approach only)
*** do #9.90, p442
*** do #9.92, p442
*** do #9.94, p443
The One-Sample t-Test for a Population Mean
(P-Value Approach)
Assumptions
1. Normal population or large sample
2.  unknown
Step 1. The null hypothesis is  = o and the alternative hypothesis is
Ha: o
or Ha: o or Ha: o
(two-tailed)
(left-tailed)
(right-tailed)
Step 2. Decide on the significance level, .
Step 3. Compute the value of the test statistic, and denote the value t o.
t
x  o
s
n
Step 4. Use the calculator to find the p-value. (STAT, TESTS, 2:T-test)
Step 5. If P  , reject Ho; otherwise, do not reject Ho.
Step 6. Interpret the results of the hypothesis test.
*** do 9.90, 9.92, and 9.94 using the p-value approach
Using the TI-83 for a one-sample t-test
STAT, TESTS, 2:T-test
Interpret results using p-value:
If P  , reject Ho; otherwise, do not reject Ho.
*** do 9.90, 9.92, and 9.94 using the calculator