10.1Hypothesis Testing Objective: set up null and alternate hypotheses

Define each of the following.  Population mean  Sample mean  Population standard deviation  Sample standard deviation  Standard error of the mean

Process  A claim is made  Evidence is collected to test the claim  Data are analyzed to decide the validity of the claim  State conclusions

Hypothesis a statement or claim regarding a characteristic of a population Hypothesis testing a procedure used to test claims regarding a characteristic of a population – it can be based on sample evidence and probability Level of significance (α) the probability of making a Type I error

Null hypothesis(H 0 ) is a statement to be tested. It is assumed true until evidence indicates otherwise. Alternative hypothesis(H 1 ) is a claim to be tested. We are trying to find evidence for the alternative hypothesis. Three ways to set up null and alternative hypotheses: Two-tailed test Left-tailed test Right-tailed test

According to the Statistical Abstract of the United States, the mean outstanding credit card debt per cardholder was $4277 in A consumer credit counselor believes that the mean is now more than the 2000 amount. The US Census Bureau reported that the mean annual salary in 2002 was $51,194 for an individual whose highest degree was a bachelor's. A government economist believes that the mean is different today. In 1997, 39.4% of females had ordered merchandise or services by phone in the last 12 months. A market research analyst believes that the percentage has declined because of Internet purchases.

Determine the null and alternative hypotheses. State whether the test is two-tailed, right- tailed, or left-tailed. The Medco pharmaceutical company has just developed a new antibiotic for children. Among the competing antibiotics, 2% of children who take the drug experience headaches as a side effect. A researcher for the Food and Drug Administration wishes to test the claim that the percentage of children taking the new antibiotic who experience headaches as a side effect is more than 2%.

The Blue Book value of a used 3-year-old Chevy Corvette is $37,000. Grand wishes to test the claim that the mean price of a used 3- year-old Chevy Corvette in the Miami area is different from $37,000. The standard deviation of the contents in a 64- ounce bottle of detergent using an old filling machine was known to be 0.23 ounce. The company purchased a new filling machine and wants to test the claim that the standard deviation for the new filling machine is less than 0.23 ounce.

There are four possible outcomes from hypothesis testing. H 0 is TRUEH 1 is TRUE Do not reject H 0 Correct Conclusion Type II Error Reject H 0 Type I Error Correct Conclusion

α = P(Type I error) rejecting the null hypothesis when it is true β = P(Type II error) not rejecting the null hypothesis when the alternative is true We choose significance levels depending on the consequences of making a Type I error. If severe, we set α = If the consequences are not as severe, a higher level can be chosen, such as 0.05 or 0.10.

After analyzing the evidence, a decision is made to reject or not reject the null hypothesis. Suppose the sample evidence indicates that the null hypothesis is rejected. State the conclusion. There is sufficient evidence to support the claim. Suppose the sample evidence indicates that the null hypothesis is not rejected. State the conclusion. There is not sufficient evidence to support the claim.

 Page 511 – , 15 – 39 by 3