Chapter 11: Q. 11.114 (page 450)

Racial Crossover. Refer to Exercise $11.108$ and find and interpret a $95 %$ confidence interval for the difference between the stroke incidences of white and African-American elderly.

Short Answer

Expert verified

There is $95 %$ the interval for the difference between the proportion is $(- 0.029, 0.015)$

Step by step solution

Given Information

The given values are,

$x_{1} = 529, n_{1} = 4989, x_{2} = 103, n_{2} = 906 .$

Explanation

The formula for ${\tilde{p}}_{1}$ is given by,

${\tilde{p}}_{1} = \frac{x_{1}}{n_{1}}$

The formula for ${\tilde{p}}_{2}$ is given by,

${\tilde{p}}_{2} = \frac{x_{2}}{n_{2}}$

The formula for $z,$ is given by,

$z = \frac{{\tilde{p}}_{1} - {\tilde{p}}_{2}}{\sqrt{{\tilde{p}}_{p} (1 - {\tilde{p}}_{p})} \sqrt{\frac{1}{n_{1}} + \frac{1}{m_{2}}}}$

The value of ${\tilde{p}}_{1}$ is calculated as,

${\tilde{p}}_{1} = \frac{x_{1}}{n_{1}} = \frac{529}{4989} = 0.106$

The value of ${\tilde{p}}_{2}$ is calculated as,

${\tilde{p}}_{2} = \frac{x_{2}}{n_{2}} = \frac{103}{906} = 0.113$

The critical value of $Z$ for two-tail test and $5 %$ level of significance is $1.96$ .

The $95 %$ confidence interval is.

$({\tilde{p}}_{1} - {\tilde{p}}_{2}) \pm z_{\frac{a}{2}} \sqrt{\frac{{\tilde{p}}_{1} (1 - {\tilde{p}}_{1})}{n_{1}} + \frac{{\tilde{p}}_{1} (1 - {\tilde{p}}_{1})}{n_{2}}} = (0.106 - 0.113)$

$\pm 1.96 \sqrt{\frac{0.106 (1 - 0.106)}{4989} + \frac{0.113 (1 - 0.113)}{906}}$

$= - 0.007 \pm 0.022$

Therefore, there is $95 %$ interval for the difference between the proportion is $(- 0.029, 0.015)$

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Racial Crossover. Refer to Exercise $11.108$ and find and interpret a $95 %$ confidence interval for the difference between the stroke incidences of white and African-American elderly.

Short Answer

Step by step solution

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Explanation

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Racial Crossover. Refer to Exercise 11.108 and find and interpret a 95% confidence interval for the difference between the stroke incidences of white and African-American elderly.

Short Answer

Step by step solution

Given Information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

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Statistics

Probability and Statistics

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Racial Crossover. Refer to Exercise $11.108$ and find and interpret a $95 %$ confidence interval for the difference between the stroke incidences of white and African-American elderly.