An independent consumer group published its finding that the lifetimes of electric bulbs manufactured by BIG Corporation are approximately normally distributed with a mean of 690 days and a standard deviation of 125. BIG Corporation claims that the standard deviation of its electric bulbs is less than 125. Suppose that we want to carry out a hypothesis test to see if BIG Corporation's claim is correct. State the null hypothesis Ho and the alternative hypothesis H₁ that we would use for this test. Ho: O H₁: 0 μ 0 X O Р S O

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**Analysis of Hypothesis Testing on Light Bulb Lifetimes**

An independent consumer group published its finding that the lifetimes of electric bulbs manufactured by BIG Corporation are approximately normally distributed with a mean of 690 days and a standard deviation of 125. BIG Corporation claims that the standard deviation of its electric bulbs is less than 125. Suppose that we want to carry out a hypothesis test to see if BIG Corporation's claim is correct. State the null hypothesis \( H_0 \), and the alternative hypothesis \( H_1 \) that we would use for this test.

- **Null Hypothesis (\( H_0 \)):** The standard deviation is equal to 125.
- **Alternative Hypothesis (\( H_1 \)):** The standard deviation is less than 125.

**Diagram Explanation**

The image contains a text description for setting up the hypothesis test, followed by a section where the hypotheses are to be written. In addition, there are various mathematical symbols provided on the right side of the image, likely intended for use in constructing the hypotheses, such as:
- Statistical symbols (\( \mu, \bar{x}, p, \sigma, P \))
- Inequality symbols (\( =, \neq, <, \leq, >, \geq \))
This allows for interactive input of the relevant hypothesis information.
Transcribed Image Text:**Analysis of Hypothesis Testing on Light Bulb Lifetimes** An independent consumer group published its finding that the lifetimes of electric bulbs manufactured by BIG Corporation are approximately normally distributed with a mean of 690 days and a standard deviation of 125. BIG Corporation claims that the standard deviation of its electric bulbs is less than 125. Suppose that we want to carry out a hypothesis test to see if BIG Corporation's claim is correct. State the null hypothesis \( H_0 \), and the alternative hypothesis \( H_1 \) that we would use for this test. - **Null Hypothesis (\( H_0 \)):** The standard deviation is equal to 125. - **Alternative Hypothesis (\( H_1 \)):** The standard deviation is less than 125. **Diagram Explanation** The image contains a text description for setting up the hypothesis test, followed by a section where the hypotheses are to be written. In addition, there are various mathematical symbols provided on the right side of the image, likely intended for use in constructing the hypotheses, such as: - Statistical symbols (\( \mu, \bar{x}, p, \sigma, P \)) - Inequality symbols (\( =, \neq, <, \leq, >, \geq \)) This allows for interactive input of the relevant hypothesis information.
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