Answered: Two surgical procedures are widely used…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

Two surgical procedures are widely used to treat a certain type of cancer. To compare the success rates of the two procedures, random samples of the two types of surgical patients were obtained and the numbers of patients who showed no recurrence of the disease after a 1-year period were recorded. The data are shown in the table. How large a sample would be necessary in order to estimate the difference in the true success rates to within 0.10 with 95% confidence interval for population proportion?

	n	number of successes
Procedure A	100	95
Procedure B	100	97

Group of answer choices

n1=n2=21

n1=n2=192

n1=n2=30

n1=n2=29

Expert Solution

Step 1

Given:

$E = 0.10 p_{1} = 0.95 p_{2} = 0.97$

From the standard normal table, the value of z at 95% confidence level is 1.96.

The sample size for the difference in the true success rates is obtained as below:

$\begin{array}{rcl} n & = & \frac{z^{2}}{E^{2}} \times [p_{1} (1 - p_{1}) + p_{2} (1 - p_{2})] \\ = & \frac{1 . 96^{2}}{0 . 10^{2}} \times [0.95 \times (1 - 0.95) + 0.97 \times (1 - 0.97)] \\ = & 384.16 \times (0.0766) \\ = & 29.4266 \\ ≅ & 29 \end{array}$

Thus, the sample size required to estimate the difference in the true success rates is 29.

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