Question

Why is the Central Limit Theorem considered to be so important for inferential statistics? Consider the...

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.

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

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