The basis for using a normal probability distribution to approximate the sampling distribution of and is _____.

Question

The basis for using a normal probability distribution to approximate the sampling distribution of  and  is _____.

BlackTom AI · Accepted Answer

The question asks about the basis for using a normal probability distribution to approximate the sampling distributions of x-bar and p-hat.
Option 1: the empirical rule. This describes approximate percentages in a normal distribution (68-95-99.7%), but it does not justify why we can use a normal model for sampling distributions. It’s a descriptive rule, not a foundational justification for normality of sampling distributions.
Option 2: Bayes’ theorem. Bayes’ theorem relates prior and posterior probabilities and is central to Bayesian inference, not to why sampling distributions of sample means or proportions are approximately normal. It does not provide the basis for the normal approximation in frequentist sampling.
Option 3: Chebyshev’s theorem. Chebyshev’s inequality gives bounds on the probability that a random variable deviates from its mean for any distribution with finite variance, but it does not guarantee or explain why the sampling distribution is normal. It’s a general bound, not a justification for normality.
Option 4: the central limit theorem. The CLT states that, under mild conditions, the sampling distribution of the sample mean (and, with certain caveats, the sample proportion) tends toward a normal distribution as the sample size grows, regardless of the population distribution. This provides the theoretical foundation for using a normal model to approximate these sampling distributions, especially for larger samples.

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The basis for using a normal probability distribution to approximate the sampling distribution of and is _____.

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If repeated random samples of size 40 are taken from an infinite population, the distribution of sample means

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Check the conditions required to complete this test. Specifically, is the sampling distribution of average differences approximately normally distributed?

Which of the following is incorrect about the sampling distribution of the sample mean using the Central Limit Theorem?[Fill in the blank]

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The basis for using a normal probability distribution to approximate the sampling distribution of and is _____.

查看解析

登录即可查看完整答案

类似问题

If repeated random samples of size 40 are taken from an infinite population, the distribution of sample means

How does the normal distribution emerge? Pick between A , B and C

Can we assume that the distribution of mean lead concentrations in blood collected from repeated samples of 52 police officers to be normal?

Check the conditions required to complete this test. Specifically, is the sampling distribution of average differences approximately normally distributed?

Which of the following is incorrect about the sampling distribution of the sample mean using the Central Limit Theorem?[Fill in the blank]

更多留学生实用工具

考试浏览器助手

风格化写作助手

论文查重助手

文献引用助手

课堂转译助手

课堂笔记助手

Quiz搜索助手

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MGS2150W07 final- Requires Respondus LockDown Browser