1. No category

Aim: What is the P-value method
for hypothesis testing?
Quiz Friday
P-value
• Usually test hypotheses at the common alpha levels of
0.05 and 0.01 and sometimes 0.10
• The choice of the alpha level depends on the
seriousness of the type I error
• P-value (probability value): is the probability of getting
a sample statistic (such as the mean) or a more
extreme sample statistic in the direction of the
alternative hypothesis when the null hypothesis is true
– In other words, the P-value is the actual area under the
standard normal distribution curve representing the
probability of a particular sample statistic or a more
extreme sample statistic occurring if the null hypothesis is
true.
Procedure
1.
2.
3.
4.
5.
State the hypothesis and identity the claims
Compute the test value
Find the P-value
Make the decision
Summarize the results
Example
• A researcher wishes to test the claim that the
average age of lifeguards in Ocean City is
greater than 24 years. She selects a sample of
36 guards and find the mean of the sample to
be 24.7 years, with a standard deviation of 2
years. Is there evidence to support the claim
at α = 0.05? Use the P-value method.
Example Solution
• Step 1: State the hypotheses and identify the claim
H 0 :   24
H1 :   24
• Step 2: Compute the test value
Z
24.7  24
 2.10
2
36
• Step 3: Find the P-value (from z-table) – area under the curve
.5000  .4821  .0179
• Step 4: Make the decision
– Since the P-value is less than 0.05, the decision is to rejected the null
hypothesis
• Step 5: Summarize Results
– There is enough evidence to support the claim that the average age of
lifeguards in Ocean City is greater than 24 years.
Decision Rule When using a P-value
• If the P-value ≤ α, reject the null hypothesis
• If the P-value is > α, do not reject the null
hypothesis