document.write( "Question 1039187: A researcher finds that of 1,000 people who said they attend a religious service at least once a week, 31 stopped to help a person with car trouble. Of 1,200 people interviewed who had not attended a religious service at least once a month, 22 stopped to help a person with car trouble. At the 0.05 significance level, test the claim that the two proportions are equal.
\n" ); document.write( "HO:
\n" ); document.write( "H1:
\n" ); document.write( "Test statistic:
\n" ); document.write( "Critical Value: \n" ); document.write( "
Algebra.Com's Answer #653929 by Boreal(15235)\"\" \"About 
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Ho:religious service frequency makes no difference, p1=p2; p1=1x/week, p2=not once a month
\n" ); document.write( "Ha:there is a difference p1 NE p2
\n" ); document.write( "alpha=0.05
\n" ); document.write( "test statistic is a 2 sample proportion;
\n" ); document.write( "This is normally distributed with a critical value at the 5% level of |z|>1.96
\n" ); document.write( "Pooled sample proportion. Since the null hypothesis states that P1=P2, we use a pooled sample proportion (p) to compute the standard error of the sampling distribution.
\n" ); document.write( "p = [(p1 * n1)+(p2 * n2)] / (n1 + n2), here is
\n" ); document.write( "p1 is the sample proportion from population 1, p2 is the sample proportion from population 2, n1 is the size of sample 1, and n2 is the size of sample 2.\r
\n" ); document.write( "\n" ); document.write( "The standard error (SE) of the sampling distribution difference between two proportions.
\n" ); document.write( "SE= sqrt{[ p*( 1- p )* (1/n1) + (1/n2) }\r
\n" ); document.write( "\n" ); document.write( "Test statistic. The test statistic is a z-score (z) defined by the following equation.
\n" ); document.write( "z = (p1-p2) / SE
\n" ); document.write( "p1=0.031;p2=0.01833
\n" ); document.write( "pooled is (31+22)/2200=0.0241
\n" ); document.write( "SE is sqrt (0.0241)(0.9759)=0.006566. Be sure to compute the (1/1000)+(1/1200) before multiplying that result by the rest.
\n" ); document.write( "(pi-p2)=0.0031-0.01833=0.01267
\n" ); document.write( "divide by SE=1.9294, which is z.
\n" ); document.write( "Fail to reject the null hypothesis, p=0.0537
\n" ); document.write( "This is checked in a calculator and is essentially the same result.
\n" ); document.write( "Stat/Test/2 proportion z-test
\n" ); document.write( "Not pooling the variance is one cause of a difference, although any test statistic greater than 1.96 (or less than -1.96) will have a p-value less than 0.05
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