Determine whether the statement below makes sense or does not make sense. Explain clearly. Based on our sample, the 95% confidence interval for the mean amount of television watched by adults in a nation is 3.5 to 4.1 hours per day. Therefore, there is 95% chance that the mean for all adults in the nation will fall somewhere in this range and a 5% chance that it will not.

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**Determining the Validity of Statistical Statements**

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This educational section focuses on interpreting statistical data, specifically the 95% confidence interval for the mean amount of television watched by adults.

**Statement for Evaluation:**

"Based on our sample, the 95% confidence interval for the mean amount of television watched by adults in a nation is 3.5 to 4.1 hours per day. Therefore, there is a 95% chance that the mean for all adults in the nation will fall somewhere in this range and a 5% chance that it will not."

**Diagram Explanation:**

There is no diagram or graph associated with this topic. It is presented as a text-based multiple-choice question for validating understanding.

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**Choose the Correct Answer Below:**

- **A.** The statement makes sense. There is 95% probability that the confidence interval limits actually contain the true value of the population mean, so the probability it does not fall in this range is 100% - 95% = 5%.
  
- **B.** The statement does not make sense. The probability the population mean is greater than the upper limit is 5% and the probability it is less than the lower limit is 5%, so the probability it does not is 5% + 5% = 10%.

- **C.** The statement makes sense. There is 5% probability that the confidence interval limits do not contain the true value of the sample mean, so the probability it does not contain the true value of the population mean is also 5%.

- **D.** The statement does not make sense. The population mean is a fixed constant that either falls within the confidence interval or it does not. There is no probability associated with this.

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Analyzing the options can help clarify common misconceptions about confidence intervals and their interpretation. For educational purposes, it is crucial to understand that the confidence interval gives a range that, when sampling repeatedly, should contain the population mean 95% of the time. However, the true population mean is a fixed value and does not deviate based on the interval.
Transcribed Image Text:**Determining the Validity of Statistical Statements** --- This educational section focuses on interpreting statistical data, specifically the 95% confidence interval for the mean amount of television watched by adults. **Statement for Evaluation:** "Based on our sample, the 95% confidence interval for the mean amount of television watched by adults in a nation is 3.5 to 4.1 hours per day. Therefore, there is a 95% chance that the mean for all adults in the nation will fall somewhere in this range and a 5% chance that it will not." **Diagram Explanation:** There is no diagram or graph associated with this topic. It is presented as a text-based multiple-choice question for validating understanding. --- **Choose the Correct Answer Below:** - **A.** The statement makes sense. There is 95% probability that the confidence interval limits actually contain the true value of the population mean, so the probability it does not fall in this range is 100% - 95% = 5%. - **B.** The statement does not make sense. The probability the population mean is greater than the upper limit is 5% and the probability it is less than the lower limit is 5%, so the probability it does not is 5% + 5% = 10%. - **C.** The statement makes sense. There is 5% probability that the confidence interval limits do not contain the true value of the sample mean, so the probability it does not contain the true value of the population mean is also 5%. - **D.** The statement does not make sense. The population mean is a fixed constant that either falls within the confidence interval or it does not. There is no probability associated with this. --- Analyzing the options can help clarify common misconceptions about confidence intervals and their interpretation. For educational purposes, it is crucial to understand that the confidence interval gives a range that, when sampling repeatedly, should contain the population mean 95% of the time. However, the true population mean is a fixed value and does not deviate based on the interval.
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