9.5 - P-Values - Another Approach to Hypothesis Testing.
P-Value (Observed Significance Level or Probability Value)
To obtain the P-value of a hypothesis test, we assume that the null
hypothesis is true and compute the probability of observing a value of the
test statistic as extreme or more extreme than that observed.
Obtaining p-Values for a One-Sample z-Test
Find the test statistic by using the formula
z
x  o

n
(1) Find the p-value if the test statistic is z = 2.32 in a two tailed test.
(2) Find the p-value if the test statistic is z = 1.57 in a right tailed test.
(3) Find the p-value if the test statistic is z = -2.87 in a left tailed test.
*** do # 9.72, 9.74, p. 431
Decision Criterion for a Hypothesis Test Using the P-Value
If the P-value is less than or equal to the specified significance level, reject
the null hypothesis; otherwise, do not reject the null hypothesis.
*** do # 9.68, p. 431
The One-Sample z-Test for a Population Mean
(P-Value Approach)
Assumptions
1. Normal population or large sample
2.  known
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 zo.
z
x  o

n
Step 4. Use table II to obtain the p-value
*** see graphs page 426
Step 5. If P  , reject Ho; otherwise, do not reject Ho.
Step 6. Interpret the results of the hypothesis test.
*** see example 9.14, p. 426
Using the TI-83 for a one-sample z-test
*** do example 9.15, p. 429
Enter the data from table 9.10, page 427 into List L1 (if there is no data,
ignore this step)
Press STAT
Arrow right to TESTS
Select 1:Z-Test by pressing ENTER
Select Data by pressing ENTER (If there is no data, select Stats)
Arrow down, type the value for o, and press ENTER
Type the value for , and press ENTER
Indicate L1 for the list (If there is no data, this option will not be available)
Select <o by pressing ENTER (this selection is done according to Ha)
Arrow down, and select CALCULATE by pressing ENTER
Interpret results using the p-value
*** do # 9.76, p. 431
*** do # 9.78, p. 432
*** do # 9.80, p. 432