1-Sample Hypothesis Tests How to set up the null and alternative hypothesis

Objective Set up the null and alternative hypothesis.

Relevance Be able to use sample statistics to test population parameters.

Hypothesis Testing…… Hypothesis – a statement that something is true. Statistical Hypothesis Test – A process by which a decision is made between 2 opposing hypotheses. The 2 opposing are a negation of each other. (That way one is always true & the other is always false). It uses sample statistics to test a claim about the value of a population parameter.

2 Types of Statistical Hypotheses…… Null Hypothesis – a statement of equality (no change); no difference between the 2 parameters. This is where the equals goes every time. Alternative Hypothesis – a specific difference; inequality

Shortcut Names…… Null Hypothesis – Ho Alternative Hypothesis - Ha

Using Words – Set up the Ho and the Ha. You are testing a new design for airbags used in cars and you are concerned they might not open properly. State the Ho and the Ha. Answer: Ho: Bags open properly. Ha: Bags do NOT open properly.

Helpful Hints…… Always place the “equals” in the Ho. Shading is based on the Ha: A. “not equal to” – two tailed test (both ends) B. “greater than” – one tailed test (right) C. “less than” – one tailed test (left) Always state the claim.

Set up the Ho and the Ha…… A medical researcher is interested in finding out whether a new medicine will have undesirable side effects. He is particularly interested in the pulse rate of patients who take the medication. The mean pulse rate is 82 beats per minute. State the hypotheses and shade. Answer: This is an “equals” and “not equals” problem. It is a two tailed test. You shade both ends of the distribution. Ho: Ha: **NOTE: You always shade the Ha. Two Tailed Test

Example…… Right Tailed Test Answer: A chemist invents an additive to increase the life of a car battery. Test the claim that the mean lifetime of the car battery is 36 months or less and state the hypotheses. Answer: This problem is testing the claim that the mean lifetime will last 36 months or less. (Less than or equal to). Ho: (Claim) Ha: NOTE: Shade to the RIGHT because you always shade the Ha. Right Tailed Test

Example…… Left Tailed Test Test the claim that the mean grade on a test is less than 87. Answer: Ho: Ha: Note: Shade to the LEFT because you always shade the Ha. Left Tailed Test

Example…… Right Tailed Test Test the claim that the variance of heights is at most 5”. Answer: Ho: Ha: NOTE: Shade to the right. Right Tailed Test

“Reject” or “Fail to Reject” the Ho…… When we test a claim, we make the assumption that the Ho is true. Therefore, at the end of the test, we state either: Reject Ho Fail to Reject Ho – We can never fully “accept” Ho; only fail to reject it.