Ina random ample of males, it was found that 23 write with their left lun217 de . In a random sample of females, it was found that 65 write with their lefand 435 o not (hased on data fiom "The Left-Handed: Their Sinister History," byFowler Cotas, Education Resources Information Center, Paper 399519). We want to0.01 sienificance level to test the dlaim that the rate of left-handedness among maies sthan that among femalesa. Tesr the claim usinga hypothesis test.b. Test the daim by construcing an appropriate confidence interval.e. Based on the reults, is the rate of left-handedness among males less than the rate of lhandedness among females?

Given that: Use left-hand to write? Male Female Yes 23 65 No 217 455 Significance level,…

Answered: Ina random ample of males, it was found…

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

Ina random ample of males, it was found that 23 write with their left lun
217 de . In a random sample of females, it was found that 65 write with their lef
and 435 o not (hased on data fiom "The Left-Handed: Their Sinister History," by
Fowler Cotas, Education Resources Information Center, Paper 399519). We want to
0.01 sienificance level to test the dlaim that the rate of left-handedness among maies s
than that among females
a. Tesr the claim usinga hypothesis test.
b. Test the daim by construcing an appropriate confidence interval.
e. Based on the reults, is the rate of left-handedness among males less than the rate of l
handedness among females?

Expert Solution

Step 1

Given that:

Use left-hand to write?	Male	Female
Yes	23	65
No	217	455

Significance level, $α = 0.01$

Step 2

Find the sample size of each gender by doing sum of "Yes" and "No":

For male, the sample size is:

$\begin{array}{rcl} n_{1} & = & 23 + 217 \\ = & 240 \end{array}$

For female, the sample size is:

$\begin{array}{rcl} n_{2} & = & 65 + 455 \\ = & 520 \end{array}$

Compute the sample proportion for males who write with their left hand by using the formula:

$\begin{array}{rcl} {\hat{p}}_{1} & = & \frac{x_{1}}{n_{1}} \\ = & \frac{23}{240} \\ = & 0.095833 \\ ≅ & 0.096 \end{array}$

Similarly, compute the sample proportion for males who write with their left hand by using the formula:

$\begin{array}{rcl} {\hat{p}}_{2} & = & \frac{x_{2}}{n_{2}} \\ = & \frac{65}{520} \\ = & 0.125 \end{array}$

(a)

State the null and alternative hypotheses:

$\begin{array}{rcl} H_{0} : p_{1} & = & p_{2} \\ H_{1} : p_{1} & < & p_{2} \end{array}$

This is left-tailed test.

Since this is test of proportions so use z-test or normal distribution.

Compute the pooled proportion by using the formula:

$\begin{array}{rcl} \hat{p} & = & \frac{x_{1} + x_{2}}{n_{1} + n_{2}} \\ = & \frac{23 + 65}{240 + 520} \\ = & 0.11578 \\ ≅ & 0.116 \end{array}$

Compute the test statistic:

$\begin{array}{rcl} z & = & \frac{({\hat{p}}_{1} - {\hat{p}}_{2}) - (p_{1} - p_{2})}{\sqrt{\hat{p} (1 - \hat{p}) (\frac{1}{n_{1}} + \frac{1}{n_{2}})}} \\ = & \frac{(0.096 - 0.125) - (0)}{\sqrt{0.116 \times (1 - 0.116) (\frac{1}{240} + \frac{1}{520})}} \\ = & - 1.16 \end{array}$