1. HYPOTHESIS TESTING `

2. Statistical Inference the methods for drawing a conclusion about the population we have sampled, while at the same time having some knowledge of the likelihood that the conclusion is incorrect. the use of the information in a sample to draw conclusions about the entire population.

3. What is a statistical hypothesis? A statistical hypothesis is a statement about one or more parameter in the model we are considering. There are two hypotheses in a statistical hypothesis testing: Null Hypothesis Alternative Hypothesis One of these statistical hypotheses corresponds to the scientific hypothesis of interest, while the other contradicts the scientific hypothesis.

4. Hypotheses The NULL: Ho and the ALTERNATIVE: Ha Ho: claim about a population that is initially assumed to be TRUE Ha: hypothesis against the Ho Ho: Jeremy is guilty of CHEATING in room 34 during the final exam Ha: Jeremy is NOT guilty of CHEATING in room 34 during the final exam

5. Types of Hypothesis Test Non-Directional Alternative Hypothesis Directional Alternative Hypothesis

6. 6 Example: The EPA reports that Honda Civic ’ s mean emission of NOX/mi is 1.45 grams. Honda claims that their new car manufacturing process reduces the mean level of exhaust emitted by Honda Civic. State your null and alternative hypotheses to prove their claim. Ho: Ha: Honda civic ’ s NOX/mile emission has a mean of 1.45 grams (µ=1.45) Honda civic ’ s NOX/mile emission has a mean that is less than 1.45 grams (µ < 1.45)

7. 7 Example: 2 American Express wondered whether giving frequent flyer miles for every purchase would increase credit card usage. Their current mean usage per individual card holder is $2500 per year. State the hypotheses for this claim. Ho: Ha: American Express has a mean card usage of $2500/year for individual card holder (µ=$2500) American Express has a mean card usage of more than $2500/year for individual card holder (µ>$2500)

8. 8 Example:3 An insurance company is reviewing its current policy rates. When originally setting the rates, they believed that the average claim amount was $1800. They are concerned that the true mean is actually higher than this set amount, which means they could potentially lose a lot of money. State the hypotheses for this claim. Ho: Ha: The insurance company ’ s average claim is $1800 (µ=$1800) The insurance company ’ s average claim is more than $1800 (µ>$1800)