Hypothesis Testing for the Mean ztest Large Samples

Hypothesis Testing for the Mean z-test! Large Samples

Decision Rule Based on P-value • If Examples: 1. The P-value for a hypothesis test is P = 0. 023. What is your decision if the level of significance is a. ? Reject the null hypothesis b. ? Fail to reject the null hypothesis

Finding the P-value for a Hypothesis Test After determining the hypothesis test’s standardized test statistic and the test statistic’s corresponding area, do one of the following to find the P-value. a. For a left-tailed test, P = (Area in left tail). b. For a right-tailed test, P = (Area in right tail) c. For a two-tailed test, P = 2(Area in tail of test statistic)

Example #1 1. Find the P-value for a left-tailed hypothesis test with a test statistic of z = -1. 48. Decide whether to reject H 0 if the level of significance is = 0. 05. Solution: P = 0. 069 P(z = -1. 48) = 0. 069 Since p > 0. 05, fail to reject the H 0. Evidence at the 5% level supports the null hypothesis.

Example #2 Find the P-value for a two-tailed hypothesis test with a test statistic of z = 2. 31. Decide whether to reject H 0 if the level of significance is = 0. 01. Solution P(z > 2. 31) = 0. 0104 P= 2(Area in both tails) =. 0219 P = 0. 0104 Fail to reject the H 0, there is enough evidence to support the H 0 at the 1% level since p > 0. 01.

Steps for z-Test

Changing the level of significance to a z- score in order to find the critical value. • Specify the level of significance • Decide whether the tail is left tailed, right tailed, or two tailed. • Find the critical value(s) z 0. – Left tailed, find the z-score that corresponds to an area of – Right tailed, find the z-score that corresponds to an area of 1 – – Two tailed, find the z-scores that correspond to and 1 -

NOW YOU GET TO DO PRACTICE 7. 2!