Actual State of Affairs The UNKNOWN TRUTH H is TRUE H is FALSE Decision Do not

# Actual state of affairs the unknown truth h is true h

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Actual State of Affairs The UNKNOWN TRUTH H 0 is TRUE H 0 is FALSE Decision Do not reject H 0 Correct Decision Type II Error Reject H 0 Type I Error Correct Decision OIS 2340 Business Statistics Estimating Population Parameters 5 Three Methods for Conducting a Hypothesis Test 1. Compare a test-statistic computed from the sample data with a critical z-value (or t-value)based upon the level of significance. (Note: t-values are used when the population standard deviation is unknown.) z z OIS 2340 Business Statistics Estimating Population Parameters 6 2. Compare a sample statistic (x-bar or p-bar) to a critical test statistic valuethat corresponds to the upper or lower confidence limit. Critical Test Statistic Value for Mean (σ known): z n Critical Test Statistic Value for Mean (σ unknown): t n Critical Test Statistic Value for Proportion: 1 z n ADVANTAGE: Includes the original contextual units. Example: Consider the following hypothesis test: H o : µ = 15 H A : µ ≠ 15 A sample of 50 provided a sample mean of 14.15. The population standard deviation is 3. Use α = 0.05. OIS 2340 Business Statistics Estimating Population Parameters 7 3. Use the p-value . The p-value is the observed level of significance, or the actual probability of making a Type I error. ADVANTAGE: Easy with technology. DISADVANTAGE: More complicated without technology. Example: Consider the following hypothesis test: H o : µ > 80 H A : µ < 80 A sample of 100 provided a sample mean of 75.5. The population standard deviation is 12. Use α = 0.01. OIS 2340 Business Statistics Estimating Population Parameters 8  #### You've reached the end of your free preview.

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• Fall '11
• Statistics, Statistical hypothesis testing, Type I and type II errors
• • • 