You wish to test the following claim that π1>π2 . You use a significance level of 0.02. Ho:π1=π2 Ha:π1>π2 You obtain 333 successes in a sample of size n1=473 from the first population. You obtain 362 successes in a sample of size n2=603 from the second population. Use the Theory-based inference applet to conduct this test of significance. (a) What is the z-score for this sample? z-score = (Report answer accurate to two decimal places.) (b) What is the p-value for this sample? p-value = (Report answer accurate to four decimal places.) (c) The p-value is... less than (or equal to) α greater than α (d) This p-value leads to the following conclusion: we have statistically significant evidence to support the alternative hypothesis the null hypothesis is true the null hypothesis is plausible the alternative hypothesis is true (e) As such, the final conclusion is that... We conclude that the first population proportion is equal to the second population proportion. We conclude that the first population proportion is greater than the second population proportion. We have statistically significant evidence that the first population proportion is greater than the second population proportion. It is plausible that the first population proportion is equal to the second population proportion.

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 that π1>π2 . You use a significance level of 0.02.

Ho:π1=π2
Ha:π1>π2

You obtain 333 successes in a sample of size n1=473 from the first population. You obtain 362 successes in a sample of size n2=603

from the second population. Use the Theory-based inference applet to conduct this test of significance.

(a) What is the z-score for this sample?
z-score = (Report answer accurate to two decimal places.)

(b) What is the p-value for this sample?
p-value = (Report answer accurate to four decimal places.)

(c) The p-value is...

less than (or equal to) α

greater than α

(d) This p-value leads to the following conclusion:

we have statistically significant evidence to support the alternative hypothesis
the null hypothesis is true
the null hypothesis is plausible
the alternative hypothesis is true

(e) As such, the final conclusion is that...

We conclude that the first population proportion is equal to the second population proportion.
We conclude that the first population proportion is greater than the second population proportion.
We have statistically significant evidence that the first population proportion is greater than the second population proportion.
It is plausible that the first population proportion is equal to the second population proportion.

Expert Solution

Step 1

Given that, X1= 333 successes in a sample of size n1=473 from the first population and X2= 362 successes in a sample of size n2=603 from the second population.