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
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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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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