Section 9.2 Hypothesis Testing Proportions P-Value.

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Presentation transcript:

Section 9.2 Hypothesis Testing Proportions P-Value

What type of test is it?

%Left-tailedRight-tailedTwo-tailed

Steps to Solve the Problem: Step 1: Define the hypothesis Step 2: Compute the value of the z test statistic or the P-value Step 3: Determine if the hypothesis is one-tailed or two-tailed Step 4: Compare the z-test statistic to the z for the α or compare the P-value of the z- test statistic to the α. Step 5: Make the decision based on the decision rules. Step 6: Determine the conclusion. State the decision in terms of the claim being tested.

Step 3: One-tailed or two-tailed? Since the problem states “less than” the hypothesis is one-tailed. Step 4: Since the confidence level is 95% we can use an α of.05 or the z-score of (this is negative since it is left tailed) Since the test statistic is -0.88, we can compare this to , or we can find the p-value of.1894 and compare it to.05. In both situations the test statistic is greater than the confidence level.

Step 5: Since the test statistic is greater than the confidence level, we will fail to reject the null. Meaning there is not sufficient evidence to support the claim.

The z-score for the.10 significance level is Since 2.23 is greater it falls in the rejection region. The P-value for 2.33 is Since this value is less than.10 it falls in the rejection region. NOTE: Since this is two-tailed, for comparing the p-values you must divide the significance level by 2.