Unit 8 Section 8-3 – Day 2

8-3: P-Value Method for Hypothesis Testing  Instead of giving an α value, some statistical situations might alternatively use a P-value for hypothesis testing.  P-value (or probability value) – 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.  The actual area under the standard normal distribution curve representing the probability of a particular sample statistic or a more extreme sample statistic occurring when the null hypothesis is true.

 The P-value for the z test can be found by using the z score table.  Find the corresponding area for the z score, then subtract it from to get the P-value.  If the P-value is less than α, then reject the null hypothesis.  If the P-value is greater than α, then do not reject the null hypothesis.  Remember : for a two tailed test you need to double the value for the area since there are two equally sized tails. Section 8-3

Steps for the P-Value Method  State the hypotheses and identify the claim.  Compute the test value  Find the P-value  Make the decision  Summarize the results Section 8-3

Example 1: 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 finds 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. Section 8-3

Example 2: A researcher claims that the average wind speed in a certain city is 8 miles per hour. A sample of 32 days has an average wind speed of 8.2 miles per hour. The standard deviation of the sample is 0.6 miles per hour. At α = 0.05, is there enough evidence to reject the claim? Use the p-value method. Section 8-3

Guidelines for P-values when α is not given If P-value is ≤ 0.01, reject the null hypothesis. The difference is highly significant. If P-value is > 0.01 but P-value is ≤ 0.05, reject the null hypothesis. The difference is significant. If P-value is > 0.05 but P-value is ≤ 0.10, consider the consequences of type I error before rejecting the null hypothesis. If P-value is > 0.10, do not reject the null hypothesis. The difference is not significant. Section 8-3

Homework:  Pg 415 : #’s 9, 11, Section 8-3