notes 38

# notes 38 - and females. From the sample proportions we...

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Comparing Two Independent Proportions Submitted by gfj100 on Wed, 11/11/2009 - 13:42 Example 3 In the same survey used for example 2, students were asked whether they think same sex marriage should be legal. We’ll compare the proportions saying yes for males and females. Notice that the response is categorical (yes or no). Step 1: null is H 0 : p 1 - p 2 = 0 and alternative is H a : p 1 - p 2 ≠ 0, where groups 1 and 2 are females and males, respectively. Minitab Output that can be used for Steps 2-5 Step 2: test statistic is given in last line of output as z = 4.43. Step 3: p-value is give as 0.000. It is the area to the right of 4.43 + area to left of -4.43 in a standard normal distribution. Steps 4 and 5: The p-value is less than .05 so we decide in favor of the alternative hypothesis. Thus we decide that the proportions thinking same-sex marriage should be legal differ for males

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Unformatted text preview: and females. From the sample proportions we females are more in favor (.737 or 73.7% for females versus .538 or 53.8% for males). Details for the &quot;two-sample z-test&quot; for comparing two proportions The test statistic used by Minitab is For Example 3, denominator The book uses a &quot;pooled version&quot; in which the two samples are combined to get a pooled proportion p. That value is used in place of both and in the part thats under the square root sign. We will use the Minitab method since the denominator in the calculation is the standard error that we could use to create conficence intervals. Just to illustrate the book method, in example 3, the pooled p-hat = (185+107)/(251+199) = 292/450 = .649. The pooled version of z works out to be z = 4.40 (and p-value is still 0.000)....
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## This note was uploaded on 05/31/2011 for the course STAT 200 taught by Professor Andyregards during the Spring '11 term at World College.

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notes 38 - and females. From the sample proportions we...

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