Answered: Explain why different conclusions were…

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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Just need the answer for part C. Part A and B are provided for context.

The report "Digital Democracy Survey"† describes a large national survey. In a representative sample of Americans ages 14 to 18 years, 45% indicated that they usually use social media while watching TV. Suppose that the sample size was 600.

(a) Is there convincing evidence that less than half of Americans ages 14 to 18 years usually use social media while watching TV? Use a significance level of 0.05.

The appropriate null and alternative hypotheses.

H₀: p = 0.5 versus H_a: p < 0.5

The test statistic and P-value.

z = -2.46 P-value = 0.0067

The conclusion in the problem context.

Reject H₀. We have convincing evidence that less than half of Americans ages 14 to 18 years usually use social media while watching TV.

(b) Suppose that the sample size had been 100 rather than 600 and that 45% of those in the sample indicated that they usually use social media while watching TV. Based on this sample of 100, is there convincing evidence that less than half of Americans ages 14 to 18 years usually use social media while watching TV? Use a significance level of 0.05.

The appropriate null and alternative hypotheses.

H₀: p = 0.5 versus H_a: p < 0.5

The test statistic and P-value.

z = -1.006 P-value = 0.1562

The conclusion in the problem context.

Fail to reject H₀. We do not have convincing evidence that less than half of Americans ages 14 to 18 years usually use social media while watching TV.

Getting blank out of 600 people responding this way as opposed to blank out of 100 provides much stronger evidence that fewer than half of Americans ages 14 to 18 years usually use social media while watching TV.

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