OneSampleZ_Estimation_Sp08_BB_nocolor

OneSampleZ_Estimation_Sp08_BB_nocolor - Outline One Sample...

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1 One Sample Z-Test Estimation Outline • 1-Sample Z-Test – Using hypothesis testing to determine significance. • Estimation – Using confidence intervals to determine significance. One Sample Z-Test • Second inferential Test • Given the CLT, Z can be used to test hypotheses regarding sample means (M) if μ AND σ are known. 1 Sample Z-Test: Formula () M M M Z µ σ =
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2 1 Sample Z-test • When to use: – When you know the population parameters, μ & σ (or just σ ) – When you know the mean of a sample Assumptions of Test* 1. Independent and random observations from participants from the population 2. Normality of population distribution If n > 30 Sampling distribution of the mean approaches normality as n increases Hypothetical Example. A researcher is interested in whether North Americans are able to identify emotions correctly in people from other cultures. It is known that, using a particular method of measurement, the accuracy ratings of adult North Americans in general are normally distributed with a mean of 82 and a variance of 20. This distribution is based on ratings made of emotions expressed by other North Americans. In the present study, however, the researcher arranges to test 50 adult North Americans rating emotions of individuals from another culture. The mean accuracy for these 50 individuals was 78. Hypothetical Example <Disclaimer> This is a hypothetical example used to portray an important statistical concept. The findings do not reflect what is typically found in similar studies.
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3 Step 1: State the Hypotheses: •H 0 : μ = M 1 : μ M Step 2: Determine the nature of the DV • Mean accuracy of the 50 participants –Rat io Step 3: Choose the appropriate test statistic • Determines null hypothesis distribution. • How do we know we’re using a 1-Sample Z-test? –Know BOTH the population mean and standard deviation – Interval/Ratio Data Step 4: Set Type I & Type II Error Rates • Type I Error: α = 0.05 • Type II Error: β = ? • In this example, we’re working with a given sample size. Therefore, we need to calculate power for THAT sample size. – We’ll come back to this step after figuring out power.
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4 Step 5: Determine the size of your sample • Know N = 50 • Need to figure out power for that sample size.
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OneSampleZ_Estimation_Sp08_BB_nocolor - Outline One Sample...

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