What is the sampling distribution of the x_bar percent means that the sample passes over the unit, where zero is true? The Census Bureau repot that households spend on average 31% of their total expenditure on housing. An association of home builders in Cleveland SRS interviews with 40 households in Greater Cleveland to know what percent of their spending goes toward housing. Suppose we know that spending on housing in Cleveland follows a normal distribution with sigma = 9.6% Standard deviantion
What is the sampling distribution of the x_bar percent means that the sample passes over the slot when the null hypothesis is true?
For most normal stress random variable X with mean μ and standard deviation σ, X ~ Normal (μ, σ) (note that in most textbooks and literature the notation is the variance, c is to say, X ~ Normal (μ, σ ²). software is normal with just the standard deviation.)
You can translate into standard normal units by:
Z = (X - μ) / σ
Where Z ~ Normal (μ = 0, σ = 1). You can then use the standard tables for normal cdf probabilities.
If you are looking at the average of a sample, then remember that for the entire sample with a sample size large enough for the average are normally distributed. This is called the central limit theorem.
If a sample size is is drawn from a population with mean μ and standard deviation σ then the sample mean Xbar is normally distributed
with μ the mean and standard deviation σ / a (n)
An applet for finding the values
http://www-stat.stanford.edu/ Nara ~ / JSM / ...
calculator
http://stattrek.com/Tables/normal.aspx
how to read charts
http://rlbroderson.tripod.com/statistics ...
In this issue, we
Xbar ~ Normal (μ = 0.31, σ ² = 0.009216 / 40)
Xbar ~ Normal (μ = 0.31, σ ² = 0.0002304)
Xbar ~ Normal (μ = 0.31, σ = 0.096 / sqrt (40))
Xbar ~ Normal (μ = 0.31, σ = 0.01517893)
Posted on April 16, 2010.
