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7 Pages

### stat400lec38

Course: STAT 400, Fall 2008
School: University of Illinois,...
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Word Count: 434

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Statistics 400 Tests about Proportions Recall: ^ Proportions: ( p = ) Y n 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 = , the sample proportion of successes ^ When n is large, the sampling distribution of p is given as follows: ^ p ~ N (p, p(1 - p ) ) n n Y n ^ ^ p (1 - p) ^...

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Coursehero >> Illinois >> University of Illinois, Urbana Champaign >> STAT 400

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Statistics 400 Tests about Proportions Recall: ^ Proportions: ( p = ) Y n 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 = , the sample proportion of successes ^ When n is large, the sampling distribution of p is given as follows: ^ p ~ N (p, p(1 - p ) ) n n Y n ^ ^ p (1 - p) ^ Standard Error of p : S .E.P^ = Large Sample Confidence Interval for a population proportion: General form: estimate margin of error ^ p z * S .E. p ^ Ping Ma STAT 400 -1- Hypothesis Testing for a Single Proportion: Step 1: Null Hypothesis: Hypothesis Note: Step 3: Test Statistic: Step 2: Alternative Step 4: Critical Region Ha: p &gt; p0 Ha: p &lt; p0 Ha: p p0 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 STAT 400 -2- Example: A claim is made that 34% of all college students have part-time jobs. You are a little skeptical of this result and decide to conduct an experiment. You get a sample of 100 college students and find that 47 of these students have part-time jobs. Conduct a hypothesis test with 95% confidence to determine whether more than 34% of college students have part time jobs. Ping Ma STAT 400 -3- Comparing 2 Proportions: Population Proportion 1 p1 p2 Sample Size n1 n2 Counts Y1 Sample Proportion ^ p1 = Y1 n1 Y2 n2 2 Y2 ^ p2 = To compare 2 proportions: You use the difference: ^ ^ 1. Difference: D = p1 - p 2 2. Mean of the difference: D = p1 - p 2 p1 (1 - p2 ) p2 (1 - p2 ) + 3. Variance of the difference: n1 n2 p1 (1 - p2 ) p2 (1 - p2 ) + 4. By CLT: D distributed as Normal( D , ) n1 n2 Ping Ma STAT 400 -4- Example: Many of the new products introduced to the market are targeted towards children. As part of a study, children in different age groups were compared to their abilities to sort toys into correct categories. Age Group 4-5 6-7 Sample Size 50 53 # who sorted correctly 10 28 Sample Proportion Test the null hypothesis that the two age groups are equally skills at sorting toys versus the ...

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