You wish to test out the fairness of a coin at a significance level of α=0.005. You obtain a sample of size 533 in which there are 303 heads, leading you to believe that the proportion of heads is more than 0.5.With hypotheses H0:p≤0.5 vs H1:p>0.5, what is/are the critical value(s)? (Report answer accurate to 2 decimal places.)What is the test statistic for this sample? (Report answer accurate to 2 decimal places but do not round in the middle of your calculations.)What is the p-value for this sample? (Report answer accurate to 4 decimal places.)Our decision is toreject the nullaccept the nullfail to reject the nullAs such, the final conclusion is thatthere is sufficient evidence to conclude that the population proportion of heads is greater than 0.5.there is not sufficient evidence to conclude that the population proportion of heads is greater than 0.5.there is sufficient evidence to conclude that the population proportion of heads is equal to 0.5.there is not sufficient evidence to conclude that the population proportion of heads is equal to 0.5.

Given, The sample proportion is,

Answered: ou wish to test out the fairness of a…

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 wish to test out the fairness of a coin at a significance level of α=0.005. You obtain a sample of size 533 in which there are 303 heads, leading you to believe that the proportion of heads is more than 0.5.

With hypotheses H0:p≤0.5 vs H1:p>0.5, what is/are the critical value(s)? (Report answer accurate to 2 decimal places.)

What is the test statistic for this sample? (Report answer accurate to 2 decimal places but do not round in the middle of your calculations.)

What is the p-value for this sample? (Report answer accurate to 4 decimal places.)

Our decision is to

reject the null
accept the null
fail to reject the null

As such, the final conclusion is that

there is sufficient evidence to conclude that the population proportion of heads is greater than 0.5.
there is not sufficient evidence to conclude that the population proportion of heads is greater than 0.5.
there is sufficient evidence to conclude that the population proportion of heads is equal to 0.5.
there is not sufficient evidence to conclude that the population proportion of heads is equal to 0.5.

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