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### 204 110.3 two prpoprtion z test

Course: MATH MATH 2040, Fall 2010
School: Utah Valley University
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Word Count: 258

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Tests 11.3 Comparing Two Proportions Our next statistical test will compare two sample proportions p1' = p2' = This test assumes large sample sizes, thus the standard normal z distribution is used. z= p1-p2 is the standard deviation for the difference between the two proportions and is calculated as follows: p1-p2 = Standard error of the difference between two proportions. If the null hypothesis is true , Ho:...

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Tests 11.3 Comparing Two Proportions Our next statistical test will compare two sample proportions p1' = p2' = This test assumes large sample sizes, thus the standard normal z distribution is used. z= p1-p2 is the standard deviation for the difference between the two proportions and is calculated as follows: p1-p2 = Standard error of the difference between two proportions. If the null hypothesis is true , Ho: p1 = p2, the formula for the above standard error can be rewritten without the subscripts and we obtain the simpler formula: Since p and q are not known we can use an estimate of p obtained by pooling the data. z= x1 x 2 n1 n2 1 1 p' q' ( + ) n1 n2 p' = q' = 1 p Example: Assume a new medical procedure is being proposed which is claimed to have a smaller chance of a serious side effect. A researcher decides test to this claim obtaining information on 1000 similar patients: The first group of 500 had the new procedure while the second group of 500 had the second procedure. The following results were observed Procedure New (1) Current(2) n 500 500 number with the serious side effect 48 85 Is the above data statistically significant that the new procedure reduces the proportion of patients who have the Serious side effect? 48 p1 = = 500 = .096 p2 = = = .170 1) Ho: p1 = p2 Ha: 2) = . 0 5 3) reject Ho if Z Z = 1.645 4) p' = = .133 q' = .867 z= 5) TI Stats 2 Prop ZTest x1 48 z = -3.446 n1 500 pval = 2.849 x10-4 x2 85 n2 500 p1<p2 PHStat 2 sample tests Z test differences in proportions Hypothesized difference 0 sample 1 nbr successes 48 sample size 500 sample 2 nbr successes 85 sample size 500 lower tailed test
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