How To Test A Hypothesis

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Elaine Brown
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1 Hypothesis Testing Null Hypothesis Start with a hypothesis! Statistical Hypothesis: a conjecture about a population parameter (not necessarily true) Null Hypothesis 2 Types of Hypotheses Alternative Hypothesis symbol: a hypothesis that states that there is no difference between a parameter and a specific value. Or that there is no difference between two parameters EXAMPLE: Alternative Hypothesis symbol: a hypothesis that states the existence of a difference between a parameter and a specific value. Or that there is a difference between two parameters DRUG TEST EXAMPLE: Since their could be 2 different side effects (raise or lower) this is called a two tailed test

hypothesis that states that there is no difference between a parameter and a specific value.

2 Battery Life A chemist invents an additive to increase the life of an automobile battery. The mean battery life is 36 months. Heating Bills A contractor wishes to lower heating bills by using a special type of insulation. The average monthly heating bill is $78. Since she is only interested in increasing battery life, this test is a right tailed test. Since she is only interested in decreasing heating bills, this test is a left tailed test. Hypotheses Two tailed Right tailed Left tailed IMPORTANT A claim can be either a null or alternative hypothesis: HOWEVER...evidence can only support an alternative hypothesis. It can also be used to reject a null hypothesis.

Since she is only interested in increasing battery life, this test is a right tailed test.

3 EXAMPLES State the null and alternative hypothesis for each conjecture affect the pulse rate of the population she Sample mean will not be exactly population mean IN PACKET If null hypothesis is true the mean of the sample will most likely not be exactly 82 2 Possibilities: 1. null is true and the difference is due to chance 2. null is false The farther away the sample mean is from the population mean, the stronger your evidence gets that the null is false. There are 4 possible outcomes of your experiment 90 vs 83 How do we draw the line?? Reject Do not reject true : Type I false Type II We need to make a decision on whether to accept or reject the null hypothesis based on how close the test value is.

null is false The farther away the sample mean is from the population mean, the stronger your evidence gets that the null is false.

4 Jury Example A type I error: occurs if you reject the null hypothesis when it is true. A type II error: occurs if you do not reject the null hypothesis when it is false. : defendant is innocent Reject Do not reject true : Type I : not innocent(guilty) false Type II Level of Significance THE ONLY WAY TO PROVE SOMETHING ABSOLUTELY IS TO USE THE ENTIRE POPULATION The maximum probability of committing a type I error. Symbolized by How large a difference is necessary to reject the null hypothesis? We use 3 significance levels: 10%, 5% and 1%

: defendant is innocent Reject Do not reject true : Type I : not innocent(guilty) false Type II Level of Significance THE ONLY WAY TO

5 Level of Significance Critical Values Critical Value... Critical/rejection region... noncritical/nonrejection region right tailed test left tailed test Find the following s non non PACKET two tailed test non Example A researcher believes a drug will lower bpm. The average of the population is 85 bpm. Write a null and alternative hypothesis and determine what a Type I and Type II error would be. Then find the cuttoff for rejecting the null hypothesis if your level of significance is 10%. Your standard deviation of your sample was 2 bpm.

researcher believes a drug will lower bpm. The average of the population is 85 bpm.

5/31/2013. Chapter 8 Hypothesis Testing. Hypothesis Testing. Hypothesis Testing. Outline. Objectives. Objectives

5/31/2013. Chapter 8 Hypothesis Testing. Hypothesis Testing. Hypothesis Testing. Outline. Objectives. Objectives C H 8A P T E R Outline 8 1 Steps in Traditional Method 8 2 z Test for a Mean 8 3 t Test for a Mean 8 4 z Test for a Proportion 8 6 Confidence Intervals and Copyright 2013 The McGraw Hill Companies, Inc.