STA_282_Ch_8_Notes_Flash_Cards

Statistics 282 with Wang at Central Michigan University

About this deck

By: Timothy Brown
Textbook:

Statistics: Informed Decisions Using Data (3rd Edition)
Created: 2010-02-25
Size: 16 flashcards
Views: 11

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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 � and standard deviation ? .

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

p? (Sample Proportion)=

x / n
where x is the number of individuals in the sample with the specified characteristic. The sample proportion, p?, 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 p is approximately normal provided np (1- p ) ? 10.
The mean of the sampling distribution of p is � p =p .
The standard deviation of the sampling distribution of p is p =sqrt(( p

standard error of the mean

The standard deviation of the sampling distribution of , ?_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, p?, 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 p? 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 p? is

�_p?=p

For a simple random sample of size n with a population of proportion p,
-The standard deviation of the sampling distribution of p? is

? p?=sqrt((p*(1-p))/(n)).

About this deck

By: Timothy Brown
Textbook:

Statistics: Informed Decisions Using Data (3rd Edition)
Created: 2010-02-25
Size: 16 flashcards
Views: 11

About StudyBlue

“I have used this website for three exams, and I see a huge difference in my test results.”
Naj