A study revealed that 65% of men surveyed supported the war in Afghanistan and 33% of women supported the war. If 100 men and 75 women were surveyed, find the 90% confidence interval for the data’s true difference in proportions.
Answer
Here we use the formula : \(SampleSize = (Z_{\alpha/2}/E)^2 \times \hat{p}\times (1- \hat{p})\)
So \({E \over{Z_{\alpha/2}}} = \sqrt{\hat{p} \times (1-\hat{p}) \over {SampleSize}}\)
and the proportion SD in the population is \(\sigma_p = \sqrt{p\times(1-p) \over n} \approx \sqrt{\hat{p}\times(1-\hat{p}) \over n} \text{ where p is the proportion of the parameter in the total population, and } \hat{p} \text{ in the sample}\)
\(\text{So here }E_{\hat{p}_1-\hat{p}_2} = {Z_{\alpha/2}\times\sigma_{\hat{p}_1-\hat{p}_2}}\text{ and }\sigma_{\hat{p}_1-\hat{p}_2}\approx \sqrt{variance_1 + variance_2} = \sqrt{{\hat(p)_1\times (1-\hat{p}_1)\over{n_1}}{+{\hat(p)_2\times (1-\hat{p}_2)\over{n_2}}}}\)
Question
A study revealed that 65% of men surveyed supported the war in Afghanistan and 33% of women supported the war. If 100 men and 75 women were surveyed, find the 90% confidence interval for the data’s true difference in proportions.
Answer
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Question
A study revealed that 65% of men surveyed supported the war in Afghanistan and 33% of women supported the war. If 100 men and 75 women were surveyed, find the 90% confidence interval for the data’s true difference in proportions.
Answer
Here we use the formula : \(SampleSize = (Z_{\alpha/2}/E)^2 \times \hat{p}\times (1- \hat{p})\)
So \({E \over{Z_{\alpha/2}}} = \sqrt{\hat{p} \times (1-\hat{p}) \over {SampleSize}}\)
and the proportion SD in the population is \(\sigma_p = \sqrt{p\times(1-p) \over n} \approx \sqrt{\hat{p}\times(1-\hat{p}) \over n} \text{ where p is the proportion of the parameter in the total population, and } \hat{p} \text{ in the sample}\)
\(\text{So here }E_{\hat{p}_1-\hat{p}_2} = {Z_{\alpha/2}\times\sigma_{\hat{p}_1-\hat{p}_2}}\text{ and }\sigma_{\hat{p}_1-\hat{p}_2}\approx \sqrt{variance_1 + variance_2} = \sqrt{{\hat(p)_1\times (1-\hat{p}_1)\over{n_1}}{+{\hat(p)_2\times (1-\hat{p}_2)\over{n_2}}}}\)
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Unknown title han it is, because the right side of the equation is actually a repeat of the left! Finding confidence intervals for two populations can be broken down to an easy three steps. Example question: <span>A study revealed that 65% of men surveyed supported the war in Afghanistan and 33% of women supported the war. If 100 men and 75 women were surveyed, find the 90% confidence interval for the data’s true difference in proportions. Step 1: Find the following variables from the information given in the question: n1 (population 1)=100 Phat1 (population 1, positive response): 65% or 0.65 Qhat1 (population 1, negative
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