### Chi-Square Test for IndependenceTo determine if the proportions $ p_1, p_2, p_3, $ and $ p_4 $ are equal, we use a chi-square test for independence. Perform this test by setting the significance level $ \alpha = 0.05 $.**Chi-Square Test Statistic:**\[ \chi^2 = 13.900 \]Decision Rule:- If the chi-square test statistic is greater than the critical value, reject the null hypothesis $ H_0 $.Result:- **Decision:** Reject $ H_0 $: independence### Confidence Interval Calculation**Task:**Compute a 95% confidence interval for the difference between $ p_1 $ and $ p_4 $. Round your answers to three decimal places. Indicate negative amounts with a minus sign.**95% Confidence Interval:**\[ ( \text{Lower bound}, \text{Upper bound} ) \](Note: The actual interval values are to be computed by the user as per the instructions and aren't provided in the image.) ### Study of Viewer Age and 11 p.m. News ViewershipA television station is conducting a study to explore the relationship between viewership of its 11 p.m. news program and viewer age. Age groups are categorized as follows: 18 years or less, 19 to 35, 36 to 54, and 55 or older. A random sample of 250 television viewers in each age group was selected, and their viewership of the 11 p.m. news was recorded. The findings are displayed in the table below:| Watch 11 p.m. News? | 18 or less | 19 to 35 | 36 to 54 | 55 or Older | Total ||---------------------|------------|----------|----------|-------------|-------|| Yes | 49 | 59 | 61 | 84 | 253 || No | 201 | 191 | 189 | 166 | 747 || Total | 250 | 250 | 250 | 250 | 1,000 |#### Hypothesis Testing- **Objective:** Test the null hypothesis $ H_0 $ that the proportions of viewers in each age group who watch the station's 11 p.m. news ($ p_1, p_2, p_3, p_4 $) are equal, implying that viewership is independent of age group.- **Method:** Perform a chi-square test for independence with a significance level $ \alpha = 0.05 $.- **Chi-Square Calculation:** \[ \chi^2 = 13.900 \]### Conclusion- **Decision:** Reject $ H_0 $ indicating dependence between viewer age group and viewership of the 11 p.m. news program.This analysis suggests that there is a statistically significant relationship between the age group of viewers and their likelihood of watching the 11 p.m. news, implying that factors related to age may influence viewership patterns.

p1 = 49/250 = 0.196 p4 = 81/250 = 0.336

Answered: A television station wishes to study…

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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