When conducting a hypothesis test that compares two independent population proportions, the following characteristics should be present:<\/p>\r\n\r\n
Comparing two proportions, like comparing two means, is common. If two estimated proportions are different, it may be due to a difference in the populations or it may be due to chance. A hypothesis test can help determine if a difference in the estimated proportions reflects a difference in the population proportions.<\/p>\r\n
Like the case of differences in sample means, we construct a sampling distribution for differences in sample proportions:<\/p>\r\n[latex]p'A=\\frac{X_{A}}{n_{A}}[\/latex] and [latex]p'\\frac{X_{B}}{X_{B}}[\/latex] are the sample proportions for the two sets of data in question [latex]X_{A}[\/latex] and [latex]X_{B}[\/latex].\r\n
The difference of two proportions follows an approximate normal distribution. Generally, the null hypothesis states that the two proportions are the same. That is, H0<\/sub><\/em>: pA<\/sub><\/em> = pB<\/sub><\/em><\/strong>. To conduct the test, we use a pooled proportion<\/span>, pc<\/sub><\/em><\/strong>.<\/p>\r\n\r\n When conducting a hypothesis test that compares two independent population proportions, the following characteristics should be present:<\/p>\n Comparing two proportions, like comparing two means, is common. If two estimated proportions are different, it may be due to a difference in the populations or it may be due to chance. A hypothesis test can help determine if a difference in the estimated proportions reflects a difference in the population proportions.<\/p>\n Like the case of differences in sample means, we construct a sampling distribution for differences in sample proportions:<\/p>\n [latex]p'A=\\frac{X_{A}}{n_{A}}[\/latex] and [latex]p'\\frac{X_{B}}{X_{B}}[\/latex] are the sample proportions for the two sets of data in question [latex]X_{A}[\/latex] and [latex]X_{B}[\/latex].<\/p>\n The difference of two proportions follows an approximate normal distribution. Generally, the null hypothesis states that the two proportions are the same. That is, H0<\/sub><\/em>: pA<\/sub><\/em> = pB<\/sub><\/em><\/strong>. To conduct the test, we use a pooled proportion<\/span>, pc<\/sub><\/em><\/strong>.<\/p>\n [latex]p_{c}=\\frac{x_{A}+x_{B}}{n_{A}+n_{B}}[\/latex]<\/p>\n <\/p>\n [latex]z=\\frac{(p'_{A}-p'_{B})-(p_{a}-p_{b})}{\\sqrt{P_{C}(1-P_{C})(\\frac{1}{n_{a}}+\\frac{1}{n_{B}})}}[\/latex]<\/p>\n <\/p>\n\n