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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 \(\sigma_p = \sqrt{p\times(1-p) \over n} \approx \sqrt{\hat{p}\times(1-\hat{p}) \over n} \text{ where p is the proportion of the parameter in the total population, and } \hat{p} \text{ in the sample}\)

\(\text{So here }E_{\hat{p}_1-\hat{p}_2} = {Z_{\alpha/2}\times\sigma_{\hat{p}_1-\hat{p}_2}}\text{ and }\sigma_{\hat{p}_1-\hat{p}_2}\approx \sqrt{variance_1 + variance_2} = \sqrt{{\hat(p)_1\times (1-\hat{p}_1)\over{n_1}}{+{\hat(p)_2\times (1-\hat{p}_2)\over{n_2}}}}\)

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 \(\sigma_p = \sqrt{p\times(1-p) \over n} \approx \sqrt{\hat{p}\times(1-\hat{p}) \over n} \text{ where p is the proportion of the parameter in the total population, and } \hat{p} \text{ in the sample}\)

\(\text{So here }E_{\hat{p}_1-\hat{p}_2} = {Z_{\alpha/2}\times\sigma_{\hat{p}_1-\hat{p}_2}}\text{ and }\sigma_{\hat{p}_1-\hat{p}_2}\approx \sqrt{variance_1 + variance_2} = \sqrt{{\hat(p)_1\times (1-\hat{p}_1)\over{n_1}}{+{\hat(p)_2\times (1-\hat{p}_2)\over{n_2}}}}\)

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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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

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

status | not learned | measured difficulty | 37% [default] | last interval [days] | |||
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repetition number in this series | 0 | memorised on | scheduled repetition | ||||

scheduled repetition interval | last repetition or drill |

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