Hypothesis Testing Proportions Testing with Proportions Examples The

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Hypothesis Testing Proportions

Hypothesis Testing Proportions

Testing with Proportions • Examples: The proportion of the country who live in poverty.

Testing with Proportions • Examples: The proportion of the country who live in poverty. The unemployment rate. The proportion of Columbia students from out-of-state. 2

Standard Deviation - Proportion 3

Standard Deviation - Proportion 3

Standard Error-Proportion • The standard error for a proportion is estimated the same way

Standard Error-Proportion • The standard error for a proportion is estimated the same way as the standard error of the mean: 4

Is proportion Immigrant Population Increasing in NYC? • Number Foreign born American Community Survey

Is proportion Immigrant Population Increasing in NYC? • Number Foreign born American Community Survey (ACS) sample 2004: 3, 169, 438 • Total NYC population ACS sample 2004: 7, 918, 562 • 2004 sample size = 65, 230 • Foreign Born in 2000 Census NYC: 2, 871, 032 • Total population 2000 Census NYC 2000: 8, 008, 278 • Formulate a hypothesis and test 5

T-test for proportion •

T-test for proportion •

 • p =. 36 Use the population proportion when available. Why? • s

• p =. 36 Use the population proportion when available. Why? • s =. 48 • s. e. = s/sqrt(n) =. 002 • T = 22. 2 • Alpha=. 05 7

Example • After a massive inventory, Central Library finds 12% of its volumes missing.

Example • After a massive inventory, Central Library finds 12% of its volumes missing. As a result, Central institutes new procedures to prevent theft. After instituting these procedures for one year, Central Library wants to know whether they are working, but it cannot afford the cost of a complete inventory. The library takes a sample of 200 books and cannot locate 14 of them. These 14 are assumed to be lost to theft. Formulate and test a hypothesis about the new procedures. 9

Example • After a massive inventory, Central Library finds 12% of its volumes missing.

Example • After a massive inventory, Central Library finds 12% of its volumes missing. As a result, Central institutes new procedures to prevent theft. After instituting these procedures for one year, Central Library wants to know whether they are working, but it cannot afford the cost of a complete inventory. The library takes a sample of 200 books and cannot locate 14 of them. These 14 are assumed to be lost to theft. Formulate and test a hypothesis about the new procedures. – – – Null hypothesis: p=. 12; alternative hypothesis: p≠. 12 s=. 324 s. e. =. 023 T=(. 07 -. 12)/. 023=-2. 18 Alpha=. 05 10

Example • If the error rate for TANF payments is greater than 5%, the

Example • If the error rate for TANF payments is greater than 5%, the federal government will cut off funding for New Jersey. The agency director takes a sample of 250 TANF recipients and finds that errors have been made in 18 cases. 1. What is your estimate of the error rate in N. J. ? 2. Place a 90% confidence interval. 3. Should the feds cutoff funds to N. J. ? 11

Example • If the error rate for TANF payments is greater than 5%, the

Example • If the error rate for TANF payments is greater than 5%, the federal government will cut off funding for New Jersey. The agency director takes a sample of 250 TANF recipients and finds that errors have been made in 18 cases. 1. What is your estimate of the error rate in N. J. ? 1. 18/250 = 7% 2. Place a 90% confidence interval. 1. 7% ±. 014*1. 645 ; 7% ±. 023 3. Should the feds cutoff funds to N. J. ? 12

STATA EXAMPLE

STATA EXAMPLE

Does rent regulation serve the poor? • US Poverty rate = 13. 5%

Does rent regulation serve the poor? • US Poverty rate = 13. 5%