Chapter 9 Hypothesis Testing Section 1 Introduction to

Chapter 9: Hypothesis Testing Section 1: Introduction to Hypothesis Testing

Example Ø A food company produces bags of peanuts weighing 336 grams (on the average). Periodically, the quality control department takes samples of peanut bags to determine whether the packaging process is under control.

Ø Ø = 336 g (process is under control) ≠ 336 g (process is not under control)

null hypothesis Ø a statement asserting no change, no difference, or no effect Ø value is often a historical value, claim, or production specification Ø usually takes the form of a statement about a population parameter Ø usually contains an equals sign Ø labeled Ho

alternate hypothesis Ø a statement that might be true instead of the null hypothesis Ø accepted when the null hypothesis is rejected Ø usually contains the symbols >, <, or ≠. Ø labeled H 1

hypothesis testing Ø procedure for choosing between hypotheses Ø gives the benefit of the doubt to the null hypothesis Ø the null hypothesis will be rejected (and alternate hypothesis accepted) only if sample data suggest beyond reasonable doubt that the null hypothesis is false

Steps in Hypothesis Testing 1. 2. 3. 4. 5. Identify the null hypothesis Ho and the alternate hypothesis H 1. Choose α, the level of significance. Calculate the test statistic. Determine the critical region. Make your decision.

Types of Hypothesis Tests Statement more is than 100 less than 100 Different Equal from 100 to 100 Null Hypothesis Ho =100 Alternate Hypothesis H 1 >100 <100 ≠ 100

Possible Decisions in a Hypothesis Test Decision Null Hypothesis Reject Ho Do Not Reject Ho True Type I Error Correct Decision False Correct Decision Type II Error

Type I Error Ø rejecting the null hypothesis when it is true Ø occurs if a test statistic falls in the critical region when Ho is actually true Ø probability of making a Type I error is called the level of significance, denoted

Type II Error Ø not rejecting the null hypothesis when it is false Ø occurs if the test statistic does not fall in the critical region when Ho is false Ø probability of making a Type II error is denoted

Critical Region and Types of Test Ø H 1: left-tailed test right-tailed test two-tailed test