QM

P Value for z problems

-left tail: z<TS (table value for negative TS) -right tail: z>TS (1- table value for positive TS -two tail: multiply the resulting tail by 2

Summary of tdf distribution

-tdf distribution is bell shaped and symmetric around 0 (asumptotic tails-get closer to the horizontal axis don't touch) -slightly broader trials than the z distribution -consists of a family of distributions where the actual shape of each depends on the degrees

As df increases the tdf distribution...

becomes similar to the z distribution, and identical to the z distribution when df approaches infinity pg. 278

if SD is known use z table

if SD is unknown (sample st.dev. is used)-use t table

CVs

ledt tailed are negative. both test is both

How to approximate the p-value for t

look ts in t-table with corresponding d.f, find two values between TS, look in first row for area for each and p-value will be between these two values. for two tailed multiply b2

Type 1 Error

probability ro reject the null or Ho (a)

Type 11 Error

probability to accept false null hypothesis (b)

Rule: p value<(less than) a "Ho"

reject

Increase sample size

standard error of the mean decreases, and width of confidence level is narrower

the degrees of freedom=df and they determine

the extent of the broadness of the tails of distribution. the fewer df the border the tails

when the width of the confidence interval is wider

the greater the confidence level

For a given confidence level and sample size n

the larger the population standard deviation the wider the confidence level

For a given confidence level and population standard dev

the smaller the sample size n the wider the confidence interval, and wider margin of error

For a given confidence level the greater the confidence level

the wider the confidence interval