Elementary Statistics 7-2

Rule of thumb for estimating sample size

Errors should be designed to make the sample size too large rather than too small

Choose between T and Z (Normal) Distributions When you don't know σ and n>30 (Sample size is greater than 30)

Use T distribution

Find the right sample size to estimate population mean μ

round to nearest larger whole number

Best point estimate of population mean is

sample mean (x̄)

Critical T value

tα/2

Round off rule for critical t value

1. Original data: one more decimal point than original data 2. Summary statistics: same # of digits as sample mean (x̄)

Requirements for building a Confidence Interval for estimating a population mean when σ is not known

1. Simple random sample 2. n>30 or population is normally distributed

Confidence Intervals

Can be used informally to compare different data sets, but should not be used for making formal and final conclusions about the equality of means

T stuff on excel

Is weird, you have to do it the two tailed way to get the right answer (so don't divide alpha by two, just keep the combined area of 1-alpha)

Choose between T and Z Distributions When you don't know σ and the population is normally distributed

Use T distribution

When Population is not normally distributed and n is less than or equal to 30.

Use a boot strapping method or nonparametric method

Choose between T and Z (Normal) Distributions When you know σ and n>30 (sample size is greater than 30)

Use normal (z) distribution

Choose between T and Z (Normal) Distributions When you know σ and population is normally distributed

Use normal (z) distribution

t distribution (student t distribution)

Used when you have small sample sizes. Changes shape depending on sample size. mean, t=0 standard deviation >1 As sample size increases, it gets closer to normal

Degrees of freedom

df=n-1

Confidence Interval for estimating population mean equation

x̄-E<μ<x̄+E x̄±E (x̄-E, x̄+E)