### Hypothesis Testing for Audience Interest in TV Shows#### Problem ContextIn a recent Super Bowl, a TV network predicted that **27% 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, an Advertising Group sampled 122 people who saw the commercials and found that 38 of them said they would watch one of the television shows.#### HypothesesTo test the network's prediction, we set up the following null and alternative hypotheses:- **Null Hypothesis ($H_0$):** $p = 0.27$- **Alternative Hypothesis ($H_a$):** $p < 0.27$#### Calculation of the Test StatisticWe will calculate the test statistic, $z$, for the given data, rounded to three decimal places.\[ z = \](Further details on how to compute the test statistic could follow this setup on the educational website, such as formulas and step-by-step solutions.)---### Steps to Calculate the Test Statistic:1. **Determine the sample proportion**: \[ \hat{p} = \frac{x}{n} = \frac{38}{122} \] 2. **Calculate the standard error**: \[ SE = \sqrt{\frac{p_0 (1 - p_0)}{n}} \] Where $p_0$ is the proportion under the null hypothesis (0.27) and $n$ is the sample size (122).3. **Compute the z-value**: \[ z = \frac{\hat{p} - p_0}{SE} \]By following these steps, you can determine the z-value to test the hypothesis that the actual proportion of interested viewers is lower than the predicted 27%.This structured explanation helps in understanding the process of hypothesis testing and gives clarity on each step involved.

Givensample size(n)=122x=38The null and alternative hypothesis is H0:p=0.27Ha:p<0.27

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

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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