Download Chapter 7 - ST-GDE

Math 116 and Math 116A– Study Guide for Chapter 7 = AGRESTI - SAMPLING DISTRIBUTIONS
Section 7.1 – Distributions of the sample proportion
1) Think on the simulation: REESES Pieces. We selected samples of size 25 from a population of
Reeses pieces in which 25% were orange. For each selected sample we counted the number of
orange pieces and determined the sample proportion. We did this MANY times and observed the
distribution of sample proportions for samples of size 25 (you can see this again in my website –
chapter 7 row, Chapter 7 APPLETS, see reeses)
2) Describe the shape, the mean and the standard deviation (standard error of the proportion) of the
distribution of sample proportions for samples of size n
3) Find z-scores in the p-hat distribution (see documents in my website)
4) Find probabilities in the p-hat distributions (se documents in my website)
5) Do you doubt a reported population proportion? Yes, no, why. (based on z-scores, based on
probabilities)
Section 7.2 – Distributions of the sample means
1) Think on the simulation done in class – also in my website – chapter 7 row, Chapter 7 APPLETS,
see sampling distributions)
2) Describe the shape, the mean and the standard deviation (standard error of the mean) of the
distribution of sample means for samples of size n
3) Find z-scores in the x-bar distribution (see documents in my website)
4) Find probabilities in the x-bar distributions (se documents in my website)
5) Central Limit theorem (to justify shape)
6) Do you doubt a reported population mean? Yes, no, why. (based on z-scores, based on probabilities)
SUMMARY FROM OTHER BOOK (it’s incomplete, you add what is missing)
SRS means simple random sample

A parameter in a statistical problem is a number that describes a population, such as the population
mean σ To estimate an unknown parameter, use a statistic calculated from a sample, such as the sample
mean

The law of large numbers states that the actually observed mean outcome
the population as the number of observations increases.

The population distribution of a variable describes the values of the variable for all individuals in a
population.

The sampling distribution of a statistic describes the values of the statistic in all possible samples of the
same size from the same population.

When the sample is an SRS from the population, the mean of the sampling distribution of the sample
mean is the same as the population mean . That is, μ is an unbiased estimator of μ.

The standard deviation of the sampling distribution of is σ/
for an SRS of size n if the population
has standard deviation σ. That is, averages are less variable than individual observations.

When the sample is an SRS from a population that has a Normal distribution, the sample mean
has a Normal distribution.

Choose an SRS of size n from any population with mean μ and finite standard deviation σ. The central
limit theorem states that when n is large the sampling distribution of is approximately Normal. That is,
averages are more Normal than individual observations. We can use the N(μ, σ/
distribution
must approach the mean μ of
also