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- StudyBlue
- Michigan
- Central Michigan University
- Statistics
- Statistics 282
- Wang
- STA_282_Ch_8_Notes_Flash_Cards

Timothy B.

Sampling Distribution of a statistic

A probability distribution for all possible values of the statistic computed from a sample of size n .

Sampling Distribution of the sample mean

is the probability distribution of all possible values of the random variable computed from a sample of size n from a population with mean µ and standard deviation σ .

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Step 1 of obtaining the sampling distribution of the mean

Obtain a simple random sample of size n

Step 2 of obtaining the sampling distribution of the mean

Compute the sample mean

Step 3 obtaining the sampling distribution of the mean

Assuming that we are sampling from a finite population (if the number of individuals in a population is a positive integer, we say the population is finite

Note for obtaining the sampling distribution of the mean

Once a particular sample is obtained, it cannot be obtained a second time

Caution: Central Limit Theorem

The Central Limit Theorem only has to do with the shape of the distribution of , not the center or spread

p̂ (Sample Proportion)=

x / n

where*x* is the number of individuals in the sample with the specified characteristic. The sample proportion, *p̂*, is a statistic that estimates the population proportion, *p*.

where

For a simple random sample of size n with a population of proportion p ,

- The shape of the sampling distribution of p is approximately normal provided np (1- p ) ≥ 10.
- The mean of the sampling distribution of p is µ p =p .
- The standard deviation of the sampling distribution of p is p =sqrt(( p

The standard deviation of the sampling distribution of , *σ*_{X}

If a random variable *X* is normally distributed, the distribution of the sample mean, , is

is normally distributed.

Central Limit Theorem

Regardless of the shape of the underlying population, the sampling distribution of becomes approximately normal as the sample size, *n*,
increases. In other words, for any population, regardless of its shape,
as the sample size increases, the shape of the distribution of the
sample mean becomes more “normal.

The sample proportion, *p̂*, is a statistic that estimates the

population proportion, *p*

For a simple random sample of size n with a population of proportion p,

-The shape of the sampling distribution of p̂ is approximately ______ provided np(1-p) ≥ 10.

-The shape of the sampling distribution of p̂ is approximately ______ provided np(1-p) ≥ 10.

normal.

For a simple random sample of size *n* with a population of proportion *p*,

The mean of the sampling distribution of* p̂* is

The mean of the sampling distribution of

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For a simple random sample of size *n* with a population of proportion *p*,

-The standard deviation of the sampling distribution of*p̂* is

-The standard deviation of the sampling distribution of

σ p̂=sqrt((p*(1-p))/(n)).

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