Stats Equations
Chapter 7: Intro to Sampling Distributions
Sampling Error = x̄ - μ
Z-Values for a sampling distribution of x̄ :
Z =
Z-Values adjusted with Finite Population Correction
Applied if: the sample is large relative to the population (n is greater than 5% of N) and sampling Is without replacement
Z =
Using the Sampling Distribution for Means
Compute the Sample Mean
Define the sampling distribution μx̄ =
Define the probability statement of interest
P(z30 will give sampling distribution that is nearly normal fairly symmetric, n>15
The sampling distribution with have:
Sampling Distribution of a Proportion
Sampling Proportion Error = p –
Sampling Distribution of P is approximated by a normal distribution if
Where this applies:
Mean =
Standard Error =
Z-Values for Proportions
Using the sample distribution for Proportions
Determine the population proportion,
Calculate the sample proportion, p
Derive the mean and standard deviation of the sampling distribution
Define the event of interest
If n and n(1- are both > 5, the convert p to z-value
Use the standard normal table to determine probability
Chapter 8: Estimating Single Population Parameters
Point and Confidence Interval Estimates for a Pop Mean
Point Estimate ± (Critical Value)(Standard Error)
Confidence interval for μ ( known)
Steps:
Define the population of interest and select a simple random sample of size n
Specify the confidence level
Compute the sample mean
Determine the standard error of the sampling distribution using
Determine the critical value, z, from the standard normal table.
Look up confidence level in standard normal table to find z value
Compute the confidence interval using ± z
Margin of Error: the amount added and subtracted to the point estimate to form the confidence interval (defines the relationship between the population parameter and the sample statistic) e = z
Confidence Interval for μ ( unkown)
Steps:
Define the population and
Sampling Error = x̄ - μ
Z-Values for a sampling distribution of x̄ :
Z =
Z-Values adjusted with Finite Population Correction
Applied if: the sample is large relative to the population (n is greater than 5% of N) and sampling Is without replacement
Z =
Using the Sampling Distribution for Means
Compute the Sample Mean
Define the sampling distribution μx̄ =
Define the probability statement of interest
P(z30 will give sampling distribution that is nearly normal fairly symmetric, n>15
The sampling distribution with have:
Sampling Distribution of a Proportion
Sampling Proportion Error = p –
Sampling Distribution of P is approximated by a normal distribution if
Where this applies:
Mean =
Standard Error =
Z-Values for Proportions
Using the sample distribution for Proportions
Determine the population proportion,
Calculate the sample proportion, p
Derive the mean and standard deviation of the sampling distribution
Define the event of interest
If n and n(1- are both > 5, the convert p to z-value
Use the standard normal table to determine probability
Chapter 8: Estimating Single Population Parameters
Point and Confidence Interval Estimates for a Pop Mean
Point Estimate ± (Critical Value)(Standard Error)
Confidence interval for μ ( known)
Steps:
Define the population of interest and select a simple random sample of size n
Specify the confidence level
Compute the sample mean
Determine the standard error of the sampling distribution using
Determine the critical value, z, from the standard normal table.
Look up confidence level in standard normal table to find z value
Compute the confidence interval using ± z
Margin of Error: the amount added and subtracted to the point estimate to form the confidence interval (defines the relationship between the population parameter and the sample statistic) e = z
Confidence Interval for μ ( unkown)
Steps:
Define the population and