# February 14 - February 14 Comparing two proportions...

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February 14 Comparing two proportions Essentially equivalent to using a chi-squared test for a 2 x 2 table. You can do a one-sided test when comparing two proportions using the normal. Chi-squared tests have no direction. Conditions for these tests 1. Samples are independent 2. Expected cell frequency must be 5 or greater (at least 5). 3. Require count data 4. In doing a test of independence, where possible, randomize. Examples from the text book 1. A brokerage firm wants to see whather the type of account a customer has (Silver, Gold or Platinum) affects the type of trades that customer makes (in person , by phone or on the Internet). It collects a random sample of trades made for its customers over the past year and performs a test. a. Do a chi-squared test of independence. Get a 3 x 3 table. And note that the selection unit is the trade – not the customer. 2. That brokerage firm also wants to know if the type of account affects the size of the account ( in dollars). If performs a test to see if the mean size of the accounts is the same for the 3 account types. a. This is a test for the equality of 3 means. We have not done this kind of test yet … but we soon will. 3. The academic research office at a large community college wants to see whether the distribution of courses chosen (humanities, SS, or Science) is different for its residential and nonresidential students. It assembles last semester’s data and performs a test. a. This is a test of homogeneity. We would have a 3 x 2 table (or 2 x 3) and do a chi- squared test. 4. Is the quality of a car affect by what day it was built? A car manufacturer examines a random sample of the warranty claims filed over the past two years to test whether defects are randomly distributed across days of the work week.

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