Watching TV: The 2012 general Social Survey asked a large number of people how much time they spent watching TV each day. The mean number of hours was 3.09 with a standard deviation of 2.73. Assume that in a sample of 32 teenagers, the sample standard deviation of daily TV time is 3.2 hours, and that the population of TV watching times is normally distributed. Can you conclude that the population standard deviation of TV watching times for teenagers is greater than 2.73 ? Use the a= 0.01 level of significance. Part 1 of 5 State the appropriate null and alternate hypotheses. 2.73 H1:0 > . 2.73 This hypothesis test is a right-tailed ▼ test. Part: 1/5 Part 2 of 5 Find the critical value. Round the answer to three decimal places. For a-0.01 , the critical value is

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### Watching TV: Statistical Hypothesis Testing

**Context:** 

The 2012 General Social Survey asked a large number of people how much time they spent watching TV each day. According to the survey:
- The mean number of hours was 3.09.
- The standard deviation was 2.73.
  
Consider a sample of 32 teenagers where:
- The sample standard deviation of daily TV time is 3.2 hours.
- Assume the population of TV watching times is normally distributed.

**Objective:**
Can we conclude that the population standard deviation of TV watching times for teenagers is greater than 2.73 at a significance level of \( \alpha = 0.01 \)?

**Part 1 of 5: Stating Hypotheses**

**Null Hypothesis ( \( H_0 \) ):** 
\[ \sigma = 2.73 \]

**Alternative Hypothesis ( \( H_1 \) ):** 
\[ \sigma > 2.73 \]

This hypothesis test is a **right-tailed** test.

---

**Part 2 of 5: Finding the Critical Value**

To find the critical value for \( \alpha = 0.01 \), round the answer to three decimal places.

- For \( \alpha = 0.01 \), the critical value is 

---

**Visual Representation:**
The page also contains an indication of progress, showing that the user is currently on Part 1 of 5, and includes a loading bar partially filled in blue to represent the completion ratio of 1/5.

**Instructions:**
- Follow the steps carefully to complete the hypothesis test.
- State hypotheses clearly and determine the critical values with appropriate rounding for precise results.

**Note:**
Subsequent steps will involve calculating test statistics, comparing them with the critical value, and making a decision to accept or reject the null hypothesis based on the results.

**Graphs/Diagrams:**
There are no graphs or diagrams presented in this part of the activity. The document is focused on the written statistical hypothesis and the initial steps of hypothesis testing.
Transcribed Image Text:### Watching TV: Statistical Hypothesis Testing **Context:** The 2012 General Social Survey asked a large number of people how much time they spent watching TV each day. According to the survey: - The mean number of hours was 3.09. - The standard deviation was 2.73. Consider a sample of 32 teenagers where: - The sample standard deviation of daily TV time is 3.2 hours. - Assume the population of TV watching times is normally distributed. **Objective:** Can we conclude that the population standard deviation of TV watching times for teenagers is greater than 2.73 at a significance level of \( \alpha = 0.01 \)? **Part 1 of 5: Stating Hypotheses** **Null Hypothesis ( \( H_0 \) ):** \[ \sigma = 2.73 \] **Alternative Hypothesis ( \( H_1 \) ):** \[ \sigma > 2.73 \] This hypothesis test is a **right-tailed** test. --- **Part 2 of 5: Finding the Critical Value** To find the critical value for \( \alpha = 0.01 \), round the answer to three decimal places. - For \( \alpha = 0.01 \), the critical value is --- **Visual Representation:** The page also contains an indication of progress, showing that the user is currently on Part 1 of 5, and includes a loading bar partially filled in blue to represent the completion ratio of 1/5. **Instructions:** - Follow the steps carefully to complete the hypothesis test. - State hypotheses clearly and determine the critical values with appropriate rounding for precise results. **Note:** Subsequent steps will involve calculating test statistics, comparing them with the critical value, and making a decision to accept or reject the null hypothesis based on the results. **Graphs/Diagrams:** There are no graphs or diagrams presented in this part of the activity. The document is focused on the written statistical hypothesis and the initial steps of hypothesis testing.
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