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Data Analysis Decision Making

In: Business and Management

Submitted By Mrtatham
Words 3650
Pages 15
Hypothesis Test for a Proportion
This lesson explains how to conduct a hypothesis test of a proportion, when the following conditions are met: * The sampling method is simple random sampling. * Each sample point can result in just two possible outcomes. We call one of these outcomes a success and the other, a failure. * The sample includes at least 10 successes and 10 failures. (Some texts say that 5 successes and 5 failures are enough.) * The population size is at least 10 times as big as the sample size.
This approach consists of four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results.
State the Hypotheses
Every hypothesis test requires the analyst to state a null hypothesis and an alternative hypothesis. The hypotheses are stated in such a way that they are mutually exclusive. That is, if one is true, the other must be false; and vice versa.
Formulate an Analysis Plan
The analysis plan describes how to use sample data to accept or reject the null hypothesis. It should specify the following elements. * Significance level. Often, researchers choose significance levels equal to 0.01, 0.05, or 0.10; but any value between 0 and 1 can be used. * Test method. Use the one-sample z-test to determine whether the hypothesized population proportion differs significantly from the observed sample proportion.
Analyze Sample Data
Using sample data, find the test statistic and its associated P-Value. * Standard deviation. Compute the standard deviation (σ) of the sampling distribution. σ = sqrt[ P * ( 1 - P ) / n ] where P is the hypothesized value of population proportion in the null hypothesis, and n is the sample size. * Test statistic. The test statistic is a z-score (z) defined by the following equation. z = (p - P) / σ where P is the hypothesized value of population

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