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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

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 a 0.09, do you have enough evidence

to reject the manufacturers claim? (42 p. 376) - 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

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.
- 12 p. 359
- 16

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 error occurs if a false null hypothesis

is not rejected. - Practice Identifying Errors
- 32 p. 360 (Flow Rate)

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 a. - The probability of making a type II error is

denoted by ß.

7.1 Introduction to Hypothesis Testing

- Once we have identified Ho, Ha, and a, we need to

calculate the value of a test statistic and then

use it to make a decision about Ho. - Once way to make that decision is to use the

probability value or P-value of the test. - P-value the probability of obtaining a sample

statistic with a value as extreme as or more

extreme than the 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 354. - Practice identifying the type of test
- 38 p. 360 (Clocks)
- 40 p. 360 (Lung Cancer)

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 doesnt mean we are saying Ho is true. We are

saying we do not have enough evidence to reject

Ho. - 46 p. 361 (Gas Mileage)