According to a recent poll, 74 out of 250 randomly selected U.S. adults interviewed saidthey would not be bothered if corporations collected records of their activity on theinternet.Is there sufficient evidence to conclude that more than one quarter of U.S. adults feel thisway? Test the appropriate hypotheses using a 0.01 significance level, round your teststatistic to four decimal places, and round everything else to 1 decimal places.Follow the seven-step process.

Name: According to a recent poll, 74 out of 250 randomly selected U.S. adul
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Description: According to a recent poll, 74 out of 250 randomly selected U.S. adults interviewed saidthey would not be bothered if corporations collected records of their activity on theinternet.Is there sufficient evidence to conclude that more than one quarter

Answered: According to a recent poll, 74 out 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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According to a recent poll, 74 out of 250 randomly selected U.S. adults interviewed said
they would not be bothered if corporations collected records of their activity on the
internet.
Is there sufficient evidence to conclude that more than one quarter of U.S. adults feel this
way? Test the appropriate hypotheses using a 0.01 significance level, round your test
statistic to four decimal places, and round everything else to 1 decimal places.
Follow the seven-step process.

Expert Solution

Step 1

Given:

Let n represents the number of randomly selected U.S adults(n=250).

Let X represents the number of selected adults who said that they would not be bothered if corporations collected records of their activity on the internet (X=74).

Let $\hat{p}$ represents the proportion of adults who said that they would not be bothered if corporations collected records of their activity on the internet; that is;

$\hat{p} = \frac{X}{n} = \frac{74}{250} = 0.296$

Therefore, the proportion of adults who said that they would not be bothered if corporations collected records of their activity on the internet is 0.296.

Step 1:

The statistical hypothesis that will be formed is:

H0: $P \leq 0.25 (P_{0})$

H1: $P > 0.25$

where P is the true representative of population proportion of adults who said that they would not be bothered if corporations collected records of their activity on the internet.

Step 2:

The test is right tailed test where the researcher wants to test whether more than one quarter of U.S adults would not be bothered if corporations collected records of their activity on the internet.

Step 2

Step 3:

The level of significance ( $α$ )=0.01.

Step 4:

The value of test statistics is calculated as:

$Z = \frac{\hat{p} - P_{0}}{\sqrt{\frac{P_{0} (1 - P_{0})}{n}}} = \frac{0.296 - 0.25}{\sqrt{\frac{0.25 (1 - 0.25)}{250}}} = 1.6796$

Therefore, the calculated value of test statistics is 1.6796.

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