Answered: Two samples are taken with the…

Name: Two samples are taken with the following sample means, sizes, and stan
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Description: Two samples are taken with the following sample means, sizes, and standard deviations ¯x1x¯1 = 39 ¯x2x¯2 = 35 n1n1 = 74 n2n2 = 63 s1s1 = 4 s2s2 = 5 Find a 86% confidence interval, round answers to the nearest hundredth. ____________ < μ1−μ2μ1-μ2 <___

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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Two samples are taken with the following sample means, sizes, and standard deviations ¯x1x¯1 = 39 ¯x2x¯2 = 35 n1n1 = 74 n2n2 = 63 s1s1 = 4 s2s2 = 5 Find a 86% confidence interval, round answers to the nearest hundredth. ____________ < μ1−μ2μ1-μ2 <________________

Expert Solution

Step 1

We need to construct the $86 %$ confidence interval for the difference between the population means $μ_{1} - μ_{2}$ , for the case that the population standard deviations are not known. The following information has been provided about each of the samples:

Sample Mean 1 $(\bar X_1)$ =	$39$
Sample Standard Deviation 1 $(s_1)$ =	$4$
Sample Size 1 $(N_1)$ =	$74$
Sample Mean 2 $(\bar X_2)$ =	$35$
Sample Standard Deviation 2 $(s_2)$ =	$5$
Sample Size 2 $(N_2)$ =	$63$

Based on the information provided, we assume that the population variances are equal, so then the number of degrees of freedom are $df = n_1 + n_2 -2 = 74 + 63 - 2 = 135$

$= 74 + 63 - 2$

$df = 135$ .

The critical value for $α = 0.14$ and $d f = 135$ degrees of freedom is $t_{c} = t_{1 - α /2; n - 1} = 1.485$ .

$\begin{array}{ccl} s_p & = & \displaystyle \sqrt{ \frac{(n_1-1)s_1^2 + (n_2-1)s_2^2}{n_1+n_2-2} } \\ \\ & = & \displaystyle \sqrt{ \frac{(74-1)\times 4^2 + (63-1) \times 5^2}{74 + 63 - 2} } \\ \\ & = & 4.487 \end{array}$

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