Answered: In a random sample of males, it was…

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

In a random sample of males, it was found that 29 write with their left hands and 221 do not. In a random sample of females, it was found that 70 write with their left hands and 459 do not. Use a 0.05 significance level to test the claim that the rate of left-handedness among males is less than that among females. Complete parts (a) through (c) below.

a. Test the claim using a hypothesis test.

Consider the first sample to be the sample of males and the second sample to be the sample of females. What are the null and alternative hypotheses for the hypothesis test?

H0:

p1≠p2

H1:

p1=p2

Your answer is not correct.

H0:

p1≥p2

H1:

p1≠p2

H0:

p1=p2

H1:

p1≠p2

H0:

p1≤p2

H1:

p1≠p2

H0:

p1=p2

H1:

p1<p2

This is the correct answer.

H0:

p1=p2

H1:

p1>

Identify the test statistic.

Identify the P-value.

What is the conclusion based on the hypothesis test?

The�� P-value is_____ the significance level of α=0.05, so ____ the null hypothesis. There____ evidence to support the claim that the rate of left-handedness among males is less than that among females.

b. Test the claim by constructing an appropriate confidence interval.

The 90% confidence interval is ____<p1−p2<____.

What is the conclusion based on the confidence interval?

Because the confidence interval limits _____0, it appears that the two rates of left-handedness are _____. There______ evidence to support the claim that the rate of left-handedness among males is less than that among females.

c. Based on the results, is the rate of left-handedness among males less than the rate of left-handedness among females?

A.The rate of left-handedness among males does appear to be less than the rate of left-handedness among females because the results are statistically significant.

B. The rate of left-handedness among males does appear to be less than the rate of left-handedness among females because the results are not statistically significant.

C. The rate of left-handedness among males

does not appear to be less than the rate of left-handedness among females.

D. The results are inconclusive.

Expert Solution

Step 1

Hi! Thank you for the question, As per the honor code, we are allowed to answer three sub-parts at a time so we are answering the first three as you have not mentioned which of these you are looking for. Please re-submit the question separately for the remaining sub-parts.

$L e f t h a n d e d m a l e (x_{1}) = 29 L e f t h a n d e d f e m a l e (x_{2}) = 70 T o t a l m a l e (n_{1}) = 29 + 221 = 250 T o t a l f e m a l e (n_{2}) = 70 + 459 = 529$

Sample proportion:

$\begin{array}{rcl} {\hat{p}}_{1} & = & \frac{x_{1}}{n_{1}} \\ = & \frac{29}{250} \\ = & 0.116 \\ {\hat{p}}_{2} & = & \frac{x_{2}}{n_{2}} \\ = & \frac{70}{529} \\ = & 0.132325 \\ \bar{p} & = & \frac{x_{1} + x_{2}}{n_{1} + n_{2}} \\ = & \frac{29 + 70}{250 + 529} \\ = & \frac{99}{779} \\ = & 0.127086 \end{array}$

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