Answered: In a recent Super Bowl, a TV network…

Name: In a recent Super Bowl, a TV network predicted that 17 % of the audien
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Description: In a recent Super Bowl, a TV network predicted that 17 % of the audience would express an interest in seeing one of its forthcoming television shows. The network ran commercials for these shows during the Super Bowl. The day after the Super Bowl, and

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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In a recent Super Bowl, a TV network predicted that 17 % of the audience would express an interest in seeing one of its forthcoming television shows. The network ran commercials for these shows during the Super Bowl. The day after the Super Bowl, and Advertising Group sampled 141 people who saw the commercials and found that 31 of them said they would watch one of the television shows.

Suppose you have the following null and alternative hypotheses for a test you are running:

H0:p=0.17
Ha:p>0.17

Calculate the test statistic, rounded to 3 decimal places

Expert Solution

Step 1

Let $x$ be the number of people would watch one of the television shows.

Here, $x = 31$

and $n = 141$ people who saw the commercials.

$∴ \hat{p} = \frac{x}{n} = \frac{n u m b e r o f s u c c e s s}{s a m p l e s i z e} ∴ \hat{p} = \frac{31}{141} = 0.220 a n d \hat{q} = 1 - \hat{p} = 1 - 0.220 = 0.78$

and $p_{0} = 0.17 a n d q_{0} = 1 - 0.17 = 0.83$

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