# VCU STAT 210 - Lecture28 (63 pages)

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## Lecture28

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- Pages:
- 63
- School:
- Virginia Commonwealth University
- Course:
- Stat 210 - Basic Practice of Statistics

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STAT 210 Lecture 28 Inferences on Population Proportions November 1 2017 Test 5 Monday November 6 Covers the chapter on proportions and relevant concepts from chapter VII Combination of multiple choice fill in the blank questions and problems written questions Formulas and tables provided please bring calculator and writing instrument Practice Problems Sailboat Pages 252 through 257 Relevant problems IX 9 IX 10 IX 11 IX 12 c IX 14 and IX 15 c Recommended problems IX 9 IX 10 and IX 11 Hummingbird Pages 210 through 215 Relevant problems VIII 9 VIII 10 VIII 11 VIII 12 c VIII 14 and VIII 15 c Recommended problems VIII 9 VIII 10 and VIII 11 Additional Reading and Examples Sailboat Read pages 248 through 251 Pay particular attention to pages 250 and 251 Hummingbird Read pages 206 through 209 Pay particular attention to pages 208 and 209 Statistical Inference Statistical inference involves using statistics computed from data collected in a sample to make statements about unknown population parameters This chapter we want to make inferences about the population proportion p Top Hat General Significance Testing Procedure 1 State the null and alternative hypotheses and the significance level a that is going to be used H0 Ha a General Significance Testing Procedure 1 State the null and alternative hypotheses and the significance level 2 Carry out the experiment collect the data verify the assumptions and if appropriate compute the value of the test statistic General Significance Testing Procedure 1 State the null and alternative hypotheses and the significance level 2 Carry out the experiment collect the data verify the assumptions and if appropriate compute the value of the test statistic 3 Calculate the p value or rejection region General Significance Testing Procedure 1 State the null and alternative hypotheses and state the significance level 2 Carry out the experiment collect the data verify the assumptions and compute the value of the test statistic 3 Calculate the p value 4 Make a decision on the significance of the test reject or fail to reject H0 General Significance Testing Procedure 1 State the null and alternative hypotheses and state the significance level 2 Carry out the experiment collect the data verify the assumptions and compute the value of the test statistic 3 Calculate the p value 4 Make a decision on the significance of the test reject or fail to reject H0 5 Make a conclusion statement in the words of the original problem This is the statistical inference Top Hat Point Estimate The point estimate of the population proportion p is the sample proportion p p number of successes in the sample sample size n Sampling Distribution of p Assumptions 1 Simple random sample from the population 2 A large enough sample so that the central limit theorem applies The sample is large if both np and n 1 p are greater than or equal to 10 Then the sample proportion p is distributed approximately normal with mean m p p and standard deviation sp p 1 p n p N p p 1 p n Confidence Interval A 100 C confidence interval for p is p z p 1 p n The z values are found in the table on page 340 Tests of Significance for p We hypothesize that the population proportion p equals some specified value p0 and we want to use the data in a sample to test whether this null hypothesis is appropriate or whether we should reject the null hypothesis in favor of some alternative hypothesis Null hypothesis H0 p p 0 Ha p p 0 Alternative hypothesis Ha p p 0 Ha p p 0 Example 3 It is conjectured that at any given Major League Baseball game approximately 5 of fans in attendance are attending their first Major League Baseball game Of interest is to test this claim versus the alternative that the proportion of fans in attendance at baseball games who are attending their first Major League Game is different from 0 05 What is the population of interest What is the parameter of interest Example 3 It is conjectured that at any given Major League Baseball game approximately 5 of fans in attendance are attending their first Major League Baseball game Of interest is to test this claim versus the alternative that the proportion of fans in attendance at baseball games who are attending their first Major League Game is different from 0 05 In this situation the population consists of all fans attending Major League Baseball games and the parameter of interest is p the proportion of all fans attending Major League Baseball games who are attending their first Major League Baseball game Example 3 It is conjectured that at any given Major League Baseball game approximately 5 of fans in attendance are attending their first Major League Baseball game Of interest is to test this claim versus the alternative that the proportion of fans in attendance at baseball games who are attending their first Major League Game is different from 0 05 In this situation the population consists of all fans attending Major League Baseball games and the parameter of interest is p the proportion of all fans attending Major League Baseball games who are attending their first Major League Baseball game Hypotheses H0 Ha Example 3 It is conjectured that at any given Major League Baseball game approximately 5 of fans in attendance are attending their first Major League Baseball game Of interest is to test this claim versus the alternative that the proportion of fans in attendance at baseball games who are attending their first Major League Game is different from 0 05 In this situation the population consists of all fans attending Major League Baseball games and the parameter of interest is p the proportion of all fans attending Major League Baseball games who are attending their first Major League Baseball game Hypotheses H0 p 05 Ha p 05 Tests of Significance for p The point estimate of p is the sample proportion p and if we have a simple random sample and if both np and n 1 p are greater than 10 then the sampling distribution of p is p N p p 1 p n Tests of Significance for p The point estimate of p is the sample proportion p and if we have a simple random sample and if both np and n 1 p are greater than 10 then the sampling distribution of p is p N p p 1 p n Then by the Z score transformation we obtain the standard normal statistic Z p p p 1 p n Tests of Significance for p The point estimate of p is the sample proportion p and if we have a simple random sample and if both np and n 1 p are greater than 10 then the sampling distribution of p is p N p p 1 p n Then by

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