Chapter 11: Q. 11.112 (page 477)

Vasectomies and Prostate Cancer. Refer to Exercise 11.106 and determine and interpret a $98 %$ confidence interval for the difference between the prostate cancer rates of men who have had a vasectomy and those who have not.

Short Answer

Expert verified

There is $98 %$ interval for the difference between the proportion is $(- 0.00334, - 0.0046)$

Step by step solution

Given Information

The given values are,

$x_{1} = 69, n_{1} = 21300, x_{2} = 113, n_{2} = 22000, {\tilde{p}}_{1} = 0.00324, {\tilde{p}}_{2} = 0.00514$

Explanation

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}{m_{1}} + \frac{1}{m_{2}}}}

Calculate the value of $z_{\frac{a}{2}}$ with $98 %$ confidence level is $2.33$ .

The $98 %$ confidence interval is.

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

$= \{\begin{array}{l} (0.00324 - 0.00514) \pm \\ 2.33 \sqrt{\frac{0.00324 (1 - 0.00324)}{21300} + \frac{0.00514 (1 - 0.00514)}{22000}}\} \end{array}\}$

$= - 0.0019 \pm 0.00144$

Therefore, there is $98 %$ interval for the difference between the proportion is $(- 0.00334, - 0.0046)$

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Vasectomies and Prostate Cancer. Refer to Exercise 11.106 and determine and interpret a $98 %$ confidence interval for the difference between the prostate cancer rates of men who have had a vasectomy and those who have not.

Short Answer

Step by step solution

Given Information

Explanation

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Vasectomies and Prostate Cancer. Refer to Exercise 11.106 and determine and interpret a 98% confidence interval for the difference between the prostate cancer rates of men who have had a vasectomy and those who have not.

Short Answer

Step by step solution

Given Information

Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Theoretical and Mathematical Physics

Calculus

Discrete Mathematics

Applied Mathematics

Decision Maths

Study anywhere. Anytime. Across all devices.

Vasectomies and Prostate Cancer. Refer to Exercise 11.106 and determine and interpret a $98 %$ confidence interval for the difference between the prostate cancer rates of men who have had a vasectomy and those who have not.