Question

Why is the Central Limit Theorem considered to be so important for inferential statistics? Consider the mean, standard error, and shape of the sampling distribution of the means in your answer. Also describe the role played, if any, by the underlying or population distribution, sample distribution, and sampling distribution.

Answer #1

Sol:

For large sample size,n>30

sampling distribution follows normal distribution with

xbar=

sample stddev=s=

If population distribution is not given also if the sample szies are large

we can approximate sampling distribution with normal distribution.

if sample sizes,n>30 are large samples.

Applications of CLT:

1)its critical to inferential statistics

2)In estimation, we can now determine a margin of error and a confidence interval

3)In hypothesis testing,we can make decisions with a known probability of making statistical error

1)What does the Central Limit Theorem say, and why is it so
important to inferential statistics?
2) Why would someone want to know whether a sample had more than
30 observations?
3) What is the continuity correction?
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5) What are the basic distinctions between situations in which
the binomial, poisson, and hypergeometric distributions apply?
6) Suppose you have a population with mean ? and standard
deviation ?. What can you say about the sampling...

Question Central Limit Theorem
a)According to the Central Limit Theorem, what
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b)A population has a mean ?=1800 and a standard
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sampling distribution of sample means when the sample size
n=100.

The Central Limit Theorem allows us to make predictions about
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The part that explains that there is no standardized table you
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1. The Central Limit Theorem applies to non-normal population
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2. The standard deviation of the sampling distribution will be
equal to the population standard deviation.
3. The sampling distribution will be approximately normal when
the sample size is sufficiently large.
4. The mean of the sampling distribution will be equal to the
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What is wrong with the following statement of the central limit
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Central Limit Theorem. If the random variables X1,
X2, X3, …, Xn are a random sample of size n from any distribution
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Which of the following is NOT a conclusion of the Central Limit
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sample size increases, approach a normal distribution.
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C. The distribution of the sample data will approach a normal
distribution as the sample size increases.
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What are the mean, the variance, and the standard deviation of
the sampling distribution for the sample mean?
Describe the probability distribution of the sample mean and
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standard deviation.
What is the probability that x<101.5?
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