you are required to use the correct symbols for mean of sampling distribution of sample mean,
μx-bar, in all answers to questions
you are required to use the correct symbols for standard deviation of sampling distribution of sample mean,
σx-bar, in all answers to questions
Learning Goals
declarative knowledge (definitions)
sampling distribution
sampling distribution of the sample mean
law of large numbers
central limit theorem (CLT) for mean: Suppose a random variable X
has any distribution with mean μ and standard deviation s.
Then, as the sample size n is increased, the sampling distribution of the sample mean
will become approximately normal with mean μ and standard deviation, σ/√n.
procedural knowledge
identify the sampling distribution of , i.e., shape, center, and spread
calculate probabilities based on normal curve using the empirical rule
calculate mean, μx-bar, and standard deviation (a.k.a., standard error of the mean),
σx-bar for a given sample size, n
calculate probabilities based on sample means and the sampling distribution using the TI83/84
conditional knowledge
identify the effect sample size, n, has on the shape of the sampling distribution
interpret the central limit theorem
identify how to use normalcdf appropriately for each type of question: normal distributions, and sampling distributions
identify when to use normalcdf for sampling distributions: random sample with n ≥ 30 or population is normally distributed
understand that sample statistics vary from sample to sample and confidence intervals are based on this sampling distribution
explain difference between standard deviation and standard error of the mean
understand that confidence intervals are random quantities, varying from sample to sample. Sometimes the confidence interval includes the true
population parameter and sometimes they do not. The probability the confidence interval includes the parameter is called the confidence level
given σx-bar and n, find σ
determine the effect sample size,n, has on the probability when using a sampling distribution [be careful]
explain the trade-off between confidence level and reliability of the confidence interval
Section 8.2: Distribution of the Sample Proportion
identify the effect sample size, n, has on the shape of the sampling distribution
interpret the central limit theorem
Learning Goals
declarative knowledge (definitions)
sample proportion, p-hat
procedural knowledge
identify the sampling distribution of , i.e., shape, center, and spread
convert the number of successes, x, into proportion,
calculate mean, μp-hat, and standard deviation, σp-hat for a given sample size,
n
calculate probabilities based on sample proportions and the sampling distribution using the TI83/84 [make sure to convert the number of successes, x, into proportion, ]
conditional knowledge
identify how to use normalcdf appropriately for each type of probability question: normal distributions, sampling distribution of means, and sampling distributions of proportions
identify when to use normalcdf to calculate a probability using the sampling distribution of proportions [random sample; and two conditions given below]
important notes
you are required to use the correct symbols for mean of sampling distribution of sample proportion,
μp-hat, in all answers to questions
you are required to use the correct symbols for standard deviation of sampling distribution of sample proportion,
σp-hat, in all answers to questions
Chapter 8: Required Formulas – Need to Know for Tests
Mean of the Sampling Distribution of : μ = μ
Standard Deviation of the Sampling Distribution of [a.k.a., Standard Error of the Mean]:
Standardizing a Normal Random Variable [a.k.a., z-Score for ]:
Sample Proportion:
Mean of the Sampling Distribution of : μ = p
Chapter 8: Required Formulas – Will be Given on Tests
Standard Deviation of the Sampling Distribution of :
One Condition Required for Sampling Distribution of to be Approximately Normally-Distributed:
Another Condition Required to Construct a CI for p:
n ≤ 0.05N OR 20n ≤ N