Explain why different conclusions were reached in the hypothesis tests of parts (a) and (b). 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.
Explain why different conclusions were reached in the hypothesis tests of parts (a) and (b). 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.
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 Ha: 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 Ha: 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.
(c) Explain why different conclusions were reached in the hypothesis tests of parts (a) and (b).
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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