Chapter 7 Flashcards
Sampling Distribution
The collection of all possible sample statistics we could attain from samples of the same size from a population.
The center of any sampling distribution will ____ be the value of the ______ _____, regardless of sample size
Always, population’s parameter.
What two conditions must be satisfied for the sampling distribution to be approximately normal?
1) Randomization and Independence Assumption.
2) Sufficient Sample Size Assumption
Randomization and Independence Assumption
The sampled values must have been randomly selected or result form an experiment with random assignment, and they should be independent of each other. Generally, any form of randomization will also ensure that the independence facet is satisfied.
Sufficient Sample Size Assumption
The sample size, n must be large enough that the sampling distribution is not truncated at either end. This is generally satisfied by the 15 successes and failures conditions.
Success/Failure Condition
The sample size must be big enough so that both the number of “successes,” np, and the number of “failures,” nq, are at least 15
SE{phat]= (Standard Error)
Sqrt(p(1-p)/n)= Sqrt(pq/n). Used only for categorical variables!!!
SE(xbar)=
standard deviation (s v o/ square root(N)
What are conditions under which we can say the x hat is approximately normal?
1) If the population has a normal distribution, then the sampling distribution of x hat will have a normal distribution.
2) If the data are approximately bell shaped, we can infer that the population from which it is drawn is also approximately bell shaped.
3) For larege (n greater than or equal to 30) the sampling distirbution of x hat is approximately a normal distirbution regardless of the distribution of the population.
Central Limit Theorem
For large sampling, the sampling distribution of x hat is approximately normal regardless of the distribution of the population.
When you use the ________ ________ of the _____ to estimate SE, the subsequent sampling distribution for __ uses the ___ distribution rather than the ______
sampling distribution, sample, xbar, t, normal distribution
When do we use the t distribution?
When the population standard deviation is unknown we have to use the standard deviation of the sample to calculate a “t” distribution.
What is the t distribution defined by?
Defined by degrees of freedom. IE the number of data points you need to k o9w until you can fill in the remainder of the dataset with certainty.
Standard Statistic=
Observation - mean of observation’s distribution/ (standard deviation of observation’s distribution.)
z=
x-u/o x-observation u-population mean- o-standard deviation population
