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 660 days and a standard deviation of 123.5. BIG Corporation claims that the standard deviation of its electric bulbs is less than 123.5. 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: H₁: 0 μ ê OSO ローロ |x X a Р ロメロ S ロ<ロ >O ²0

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### Hypothesis Testing for Electric 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 660 days and a standard deviation of 123.5. BIG Corporation claims that the standard deviation of its electric bulbs is less than 123.5. 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 \( H_0 \):** \(\sigma \geq 123.5\)

**Alternative Hypothesis \( H_1 \):** \(\sigma < 123.5\)

### Diagram Key:

- The diagram shows various statistical symbols, each with a corresponding checkbox:
  - **\( \mu \)**: Population mean
  - **\( \bar{x} \)**: Sample mean
  - **\( p \)**: Population proportion
  - **\( \hat{p} \)**: Sample proportion
  - **\( \sigma \)**: Population standard deviation
  - **\( s \)**: Sample standard deviation
  
Use this information to understand and state the hypotheses formally for statistical testing of claims regarding bulb lifetimes.
Transcribed Image Text:### Hypothesis Testing for Electric 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 660 days and a standard deviation of 123.5. BIG Corporation claims that the standard deviation of its electric bulbs is less than 123.5. 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 \( H_0 \):** \(\sigma \geq 123.5\) **Alternative Hypothesis \( H_1 \):** \(\sigma < 123.5\) ### Diagram Key: - The diagram shows various statistical symbols, each with a corresponding checkbox: - **\( \mu \)**: Population mean - **\( \bar{x} \)**: Sample mean - **\( p \)**: Population proportion - **\( \hat{p} \)**: Sample proportion - **\( \sigma \)**: Population standard deviation - **\( s \)**: Sample standard deviation Use this information to understand and state the hypotheses formally for statistical testing of claims regarding bulb lifetimes.
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The claim is that the standard deviation of its electric bulbs is less than 123.5.

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