8_Lecture8.1_HypothesisTesting_0225r_Spring11

8_Lecture8.1_HypothesisTesting_0225r_Spring11 - VIII....

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1 PSY207 B Spring 2011 Psychological Statistics VIII. Hypothesis Testing You should know about • Hypothesized sampling distribution • Common outcomes • Rare outcomes z test z -transformed sampling distribution • Null hypothesis • Alternative hypothesis • Decision rule • Critical z scores • Level of significance Hypothesis Testing: Example • We are interested in the effects of electric fields on IQ: • Does living near electric power lines increase or decrease IQ? Hypothesis Testing: Example • We sampled 25 people who live near power lines • IQ Scores of People Living Near a Power Lines: 100 96 117 88 121 104 103 97 115 106 102 99 131 106 73 88 98 108 108 115 97 108 102 103 102 Results M = 103.48 For IQ Scores μ = 100 σ = 16 Results M = 103.48 For IQ Scores For IQ Scores μ = 100 = 100 σ = 16 Hypothesis Testing: Example • We want to test two hypotheses: • 1. Average IQ of individuals near power lines is the same as the population average. -> Null Hypothesis • 2. Average IQs of individuals near power lines is above or below the population average. -> Alternative Hypothesis
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2 Null Hypothesis • For our example, the null hypothesis states that a mean IQ of 103.48 is not special • The null hypothesis states that • There is some “reasonable” chance or probability that one could draw a sample mean of 103.48 from a population with a mean of 100 • May be right, may be wrong Null Hypothesis • If the null hypothesis is true, there is NO evidence that electrical fields affect IQ. • If the null hypothesis is false, there IS evidence that electrical fields may affect IQs. Null Hypothesis and the Population • If the null hypothesis is true, the population you drew your sample from has a mean of 100 • If the null hypothesis is false, the population you drew your sample from does not have a mean of 100 • Instead, the population of people living next to electric power lines has a different average IQ Null Hypothesis and the Sampling Distribution • If the null hypothesis is true, the sampling distribution of the mean should be centered around the population mean of 100. • If the null hypothesis is false, the sampling distribution of the mean will be centered around some value other than 100. Sampling Distribution μ M = μ Sampling Distribution μ M = μ μ M μ μ M μ
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3 Hypothesis Testing • Hypothesis testing involves • determining if the null hypothesis is true or false • determining how probable the sample mean is given the null hypothesis • THE question • If the null hypothesis is true, how probable is our sample mean? Hypothesis Testing • The null hypothesis says: • Population Mean =100 • The sample mean is 103.48. • So, how probable is a sample mean of 103.48 if the population mean is 100? ☻☻☻☻ Population ☻☻☻ Sample Sample Means 100 98 93 103 105 Mean of Sampling Distribution AND Mean of Population Mean of Sampling Distribution AND Mean of Population Population Sample Sample Means 100 98 93 103 105 We could choose a sample mean of 103 from this sampling distribution We could choose a sample mean of 103 from
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8_Lecture8.1_HypothesisTesting_0225r_Spring11 - VIII....

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