AP STATISTICS LESSON 10 – 2 (DAY 3) TESTS FOR A POPULATION MEAN

ESSENTIAL QUESTION: How do the procedures for a one sided and two sided test differ? Objective: To become more familiar with one-sided and two-sided significance tests.

Inference toolbox Significance tests To test a claim about an unknown population parameter: Step 1: Identify the population of interest and the parameter you want to draw conclusions about state null and alternative hypotheses in words and symbols. Step 2: Choose the appropriate inference procedure. Verify the conditions for using the selected procedure. Step 3: If the conditions are met, carry out the inference procedure. Calculate the test statistic. Find the P-value. Step 4: Interpret your results in the context of the problem.

Z test for a Population Mean To test the hypothesis Ho: μ = μ0 based on an SRS of size n from a population with unknown mean μ and known standard deviation σ, compute the one-sample z statistic: In terms of a variable Z having the standard normal distribution, the P-value for a test of Ho against z = x – μ0 σ/√n

Z test for a Population Mean (continued…) These P-values are exact if the population distribution is normal and are approximately correct for large n in other cases.

Example 10.13 Page 573 Executive Blood Pressures The national Center for Health Statistics reports that the mean systolic blood pressure for males 35 to 44 years of age is 128 and the standard deviation in this population is 15. The medical director of a large company looks at the medical records of 72 executives in this age group and finds that the mean systolic blood pressure in this sample is x = 126.07 Is this evidence that the company’s executives have a different mean blood pressure than the general population? (Assume the executives have the same o = 15 as the general population of adult males).

P-value for the Two Sided Test