7.1 Introduction to Hypothesis Testing

1. 7.1 Introduction to Hypothesis Testing • Key Concepts: • Hypothesis Tests • Type I and Type II Errors • Probability Value (or P-value) of a Test • Decision Rules

2. 7.1 Introduction to Hypothesis Testing • Consider the following scenario: A fluorescent lamp manufacturer guarantees that the mean life of a certain type of lamp is at least 10,000 hours. You want to test this guarantee. To do so, you record the life of a random sample of 32 fluorescent lamps (see below). At α = 0.09, do you have enough evidence to reject the manufacturer’s claim? (#44 p. 393) 8,800 9,155 13,001 10,250 10,002 11,413 8,234 10,402 10,016 8,015 6,110 11,005 11,555 9,254 6,991 12,006 10,420 8,302 8,151 10,980 10,186 10,003 8,814 11,445 6,277 8,632 7,265 10,584 9,397 11,987 7,556 10,380

3. 7.1 Introduction to Hypothesis Testing • How can we test such claims? • Start with a pair of statistical hypotheses or statements about a population parameter. • Null Hypothesis Ho • Statistical hypothesis that contains a statement of equality like ≤, =, or ≥. • Alternative Hypothesis Ha • The complement of the null hypothesis. It is a statement that must be true of the null hypothesis if false. • Practice forming Ho and Ha. #10 p. 375 #14

4. 7.1 Introduction to Hypothesis Testing • When we conduct hypothesis tests, we always work under the assumption that the null hypothesis is true. We will reject Ho only when there is enough evidence to do so. • We need to be aware of two types of errors that may occur in a study: • A type I error occurs if a true null hypothesis is rejected. • A type II erroroccurs if a false null hypothesis is not rejected. • Practice Identifying Errors #34 p. 376 (Satellite TV)

5. 7.1 Introduction to Hypothesis Testing • Definitions and Symbols we will need later: • The probability of making a type I error is known as the significance level of the test and is denoted by α. • The probability of making a type II error is denoted by β.

6. 7.1 Introduction to Hypothesis Testing • Once we have identified Ho, Ha, and α, we need to calculate the value of a test statisticand then use it to make a decision about Ho. • Once way to make that decision is to use the probability valueor P-value of the test. P-value = the probability of obtaining a sample statistic with a value as extreme as or more extreme thanthe one determined from the sample data. • The way we calculate the P-vale of a test depends on the type of test we are working with (left-tailed, right-tailed, or two-tailed). See page 370. • Practice identifying the type of test #36 p. 376 (Clocks) #39 p. 377 (Return Rate)

7. 7.1 Introduction to Hypothesis Testing • How do we decide whether or not to reject the null hypothesis? • We use decision rules based on the P-value: • If the P-value of the test is less than or equal to the significance level, we reject Ho. • If the P-value of the test is greater than the significance level, we do not reject Ho. Note: If we do not reject the null hypothesis, it doesn’t mean we are saying Ho is true. We are saying we do not have enough evidence to reject Ho. #42 p. 377 (Shipment Weights)