Answered: You want to see if the percentage of…

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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You want to see if the percentage of cat owners is significantly less than the percentage of dog owners at a significance level of α=0.10α=0.10.

You sample 700 people and find 584 have cats. You sample an additional 739 people and find 635 have dogs.

What is the critical value for this test? (Report answer accurate to three decimal places.)
critical value =

What is the test statistic for this sample? (Report answer accurate to three decimal places.)
test statistic =

Expert Solution

Step 1

Given,

Sample size of first group n₁=700

Sample of people having cats X₁=584

Sample size of first group n₂=739

Sample of people having dogs X₂=635

Level of significance $α = 0.10$

Sample proportion of the people having cats is

$p_{1} = \frac{X_{1}}{n_{1}} = \frac{584}{700} = 0.834$

Sample proportion of the people having dogs is

$p_{2} = \frac{X_{2}}{n_{2}} = \frac{635}{739} = 0.859$

Step 2

Hypotheses:

H₀: The percentage of cat owners is not significantly less than the percentage of dog owners.

H₁: The percentage of cat owners is significantly less than the percentage of dog owners.

The test is a left tailed test.

Step 3

Critical value:

Use the EXCEL formula, "=NORMSINV(0.1)". The value obtained is -1.281.

Thus, the critical value is -1.281.

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