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MMLU / Tina’s science fair project was to estimate the mean amount of chemicals in her…

Problem

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question

Tina’s science fair project was to estimate the mean amount of chemicals in her city’s water supply. At first, she had decided to use a random sample of 15 observations. But her teacher asked her to take 35 observations. The mean and standard deviation from 35 observations turned out to be approximately the same as those from 15 observations. Is there any advantage in using 35 observations instead of 15 observations?

choices

  1. There is no advantage. Because the mean and the standard deviation are about the same, the confidence interval computed using 35 observations should be approximately the same as that computed using 15 observations.
  2. There is no advantage. In fact, the 20 extra observations will increase the likelihood of error.
  3. There is no advantage. Because she took 35 observations instead of 15 observations, the confidence interval using 35 observations will be wider than that using 15 observations.
  4. There is some advantage. Because she took 35 observations instead of 15 observations, the confidence interval using 35 observations will be narrower than that using 15 observations.

subject

high_school_statistics

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Source and history

task_id
986e0a66-e110-517a-b33f-df805fb2adf1
task_key
all--test--986e0a66-e110-517a-b33f-df805fb2adf1
task_revision_id
1
config / split
all / test

Official source

initial import