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Unformatted text preview: Statistics 400 Tests about Proportions Read: Section 8.1 Recall: Proportions: ( ) n Y p = Count the number of successes and take into account the sample Normal Approximation of proportions Draw a random sample of size n from a large population with p = P (Success); p = n Y , the sample proportion of successes When n is large, the sampling distribution of p is given as follows: p ~ N (p, n p p ) 1 (- ) Standard Error of p : n p p E S P ) 1 ( . . - = Large Sample Confidence Interval for a population proportion: General form: estimate margin of error p E S z p . . * Ping Ma Lecture 31 Fall 2005 - 1 - Hypothesis Testing for a Single Proportion: Step 1: Null Hypothesis: Step 2: Alternative Hypothesis Note: Step 3: Test Statistic: Step 4: Critical Region Ha: p p Ha: p p &lt; Ha: p p Step 5: P-values Step 6: Decision Rule: Reject Ho if: p-value &lt; Step 7: Conclusions in terms of the original problem Ping Ma Lecture 31 Fall 2005 - 2 - Example: A claim is made that 34% of all college students have part-time...
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