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Answer :
Final answer:
The Large Counts condition is satisfied in the LED bulb lifespan study because the sample size of 150 is large enough for the Central Limit Theorem to apply, leading to an approximately normal distribution of the mean lifespan. This allows for accurate verification of the manufacturer's claims using statistical methods.
Explanation:
The Large Counts condition in statistics refers to a requirement for the Central Limit Theorem which states that with a sufficiently large sample size, the sampling distribution of the mean will be approximately normally distributed, regardless of the distribution of the underlying population. When a researcher from Consumer Reports takes many random samples of 150 LED bulbs, the condition is satisfied because the sample size is large enough to assume that the distribution of the average life of the bulbs in each sample is approximately normal. This allows the researcher to use statistical methods that rely on normal distribution assumptions to verify Knell's claim about their light bulb's average life and standard deviation.
Comparing different types of lightbulbs, we see that the average lifespan of LED bulbs is significantly longer than that of CFLs and incandescent bulbs. The durability and energy efficiency of LEDs are notably superior, offering benefits like lower heat emission and the absence of hazardous substances such as mercury found in CFLs. When considering total cost, including capital and operation, LEDs and CFLs offer savings compared to incandescent bulbs, despite their higher initial cost.
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