Chapter 20 Week 9, Wednesday

Hypothesis Testing Our goal is to answer a question in one of three ways: (1) Is the proportion of Akron students that are left handed LESS THAN 25%? (2) Is the proportion of Cornell students that remind me of Sheldon from the Big Bang Theory GREATER THAN 50%? (3) Is the proportion of Statistics students who actually read the book DIFFERENT THAN 15%? We write this in the form of a null & alternative hypothesis: (1) H 0 : p = 25%H A : p < 25% (2)H 0 : p = 50%H A : p > 50% (3) H 0 : p = 15%H A : p ≠ 15%

Hypothesis Testing How we answer the question: (1) We take a representative sample of size “n” (2) Find the sample proportion ( ) (3) Compute a “test statistic” through an easy formula (4) Use the “standard normal”, Z-distribution table to find a “P-value”: (H A : p < 25%) (H A : p > 25%) (H A : p ≠ 25%)

Hypothesis Testing How we answer the question: (5) Compare the P-value to the Alpha Value (α). If PV < α then the decision is: “Reject H 0 ” and the conclusion is: “There is enough statistical evidence to conclude H A ” If PV ≥ α then the decision is: “Do Not Reject H 0 ” and the conclusion is: “There is not enough statistical evidence to conclude H A ” We are NOT saying that H 0 is true!!! We are simply saying there’s not enough evidence, given our sample, to exclude H 0 from the range of possibilities!!!

The Assumptions 1.Sample must be randomly selected, with independent data values. 2.The sample size (n) must be smaller than 10% of the population size (N). 3.Both and must exceed 10.