Determine whether the events "responding yes to the question on violence in television" and "being a woman" from a poll given below are independent. In a newspaper poll concerning violence on television, 600 people were asked, "What is your opinion of the amount of violence on prime-time television - is there too much violence on television?" Their responses are indicated in the figure given below. Yes No Don't know Total Men 162 95 23 280 Women 256 45 19 320 Total 418 140 42 600 Are the evénts independent?

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**Analysis of Poll on Violence in Television**

This section explores a survey conducted to determine whether there's a perceived excess of violence in prime-time television and examines if respondents' gender correlates to their opinions. 

**Survey Overview:**

A newspaper conducted a poll of 600 individuals asking, "What is your opinion on the amount of violence on prime-time television - is there too much violence on television?" The responses, categorized by gender, are displayed below:

**Response Data Table:**

|             | Yes | No | Don't know | Total |
|-------------|-----|----|------------|-------|
| **Men**     | 162 | 95 | 23         | 280   |
| **Women**   | 256 | 45 | 19         | 320   |
| **Total**   | 418 | 140| 42         | 600   |

**Data Breakdown:**

- **Total Respondents:** 600
- **Men Respondents:** 280
  - Yes: 162
  - No: 95
  - Don't Know: 23
- **Women Respondents:** 320
  - Yes: 256
  - No: 45
  - Don't Know: 19

**Discussion:**

Participants were categorized into two gender groups: men and women. The survey results are displayed in a table which breaks down responses to whether they think there is too much violence on television into "Yes," "No," and "Don't Know."

**Research Question:**

The core question posed is whether the events "responding yes to the question on violence in television" and "being a woman" are statistically independent. 

**Conclusion:**

To answer whether the two events are independent, a statistical test, such as the Chi-Squared test of independence, could be applied. Such an analysis would reveal whether gender significantly affects opinions on violence in television.
Transcribed Image Text:**Analysis of Poll on Violence in Television** This section explores a survey conducted to determine whether there's a perceived excess of violence in prime-time television and examines if respondents' gender correlates to their opinions. **Survey Overview:** A newspaper conducted a poll of 600 individuals asking, "What is your opinion on the amount of violence on prime-time television - is there too much violence on television?" The responses, categorized by gender, are displayed below: **Response Data Table:** | | Yes | No | Don't know | Total | |-------------|-----|----|------------|-------| | **Men** | 162 | 95 | 23 | 280 | | **Women** | 256 | 45 | 19 | 320 | | **Total** | 418 | 140| 42 | 600 | **Data Breakdown:** - **Total Respondents:** 600 - **Men Respondents:** 280 - Yes: 162 - No: 95 - Don't Know: 23 - **Women Respondents:** 320 - Yes: 256 - No: 45 - Don't Know: 19 **Discussion:** Participants were categorized into two gender groups: men and women. The survey results are displayed in a table which breaks down responses to whether they think there is too much violence on television into "Yes," "No," and "Don't Know." **Research Question:** The core question posed is whether the events "responding yes to the question on violence in television" and "being a woman" are statistically independent. **Conclusion:** To answer whether the two events are independent, a statistical test, such as the Chi-Squared test of independence, could be applied. Such an analysis would reveal whether gender significantly affects opinions on violence in television.
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