Random samples of size 17 are drawn from a population of 200 elements, mean 36, and standard deviation 8. Describe the form of the sampling distribution of the sample mean?
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Answer: D. None of these alternatives is correct
Explanation
The central limit theorem requires large sample sizes or a normally distributed population. A sample size of seventeen is relatively small when the underlying population distribution is unknown. Therefore, none of the standard normality assumptions are guaranteed to hold true here. The central limit theorem states sample means approach normality as sample size grows. Small samples require known population normality to ensure a normal sampling distribution. Finite population corrections apply when sampling without replacement from small groups.
Researchers test sample size adequacy before applying normal distribution confidence intervals. Small sample studies require non-parametric methods when population normality is unverified. Avoiding improper normality assumptions prevents erroneous statistical inference conclusions. Option A is incorrect because small sample size relative to population does not guarantee normality. Option B is wrong as sample size seventeen is too small for the central limit theorem without normality. Option C is incorrect because the option text is incomplete and cut off.
- Subject
- Mathematics
- Category
- Statistics
- Topic
- —
- Difficulty
- medium
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