Answered: You wish to test the following claim…

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

You wish to test the following claim (Ha) at a significance level of α=0.01.
Ho:p1=p2
Ha:p1<p2

You obtain 76.3% successes in a sample of size n1=520 from the first population. You obtain 83.5% successes in a sample of size n2=758 from the second population. For this test, you should NOT use the continuity correction, and you should use the normal distribution as an approximation for the binomial distribution. Find the P-Value and Test statistic.

Expert Solution

Step 1

Solution:

The null and alternative hypotheses are as follows:

Ho: p₁=p₂
Ha: p₁<p₂

Sine the alternative hypothesis contains "less than" (<) sign, it is a left tailed test.

The following information is given to us:

Sample size: n₁=520 and sample proportion: p₁ = 76.3% = 0.763

Sample size: n₂=758 and sample proportion: p₂ = 83.5% = 0.835

The formula of test statistic is as follows:

Thus, test statistic: Z = -3.195831

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