Stats_final_review

See also stats_Midterm_review

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This is a key lab and one that must be mastered. Please understand the method of maximum likelihood. This will be carried out in three ways

• NR
• Grid
• Analytical

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Testing..

• [[Stats_Lab4_notes#null-hypothesis-h_i|NULL hypothesis $H_i$]] Overall idea: Generate values, generate a line w/ values in it and c if it’s in fallen region

How to construct a test?

one sample t.test?

set.seed(523)
x = rnorm(25,10,8)
alpha = .05
t = qt(1-alpha/2.25 -1)
(mean(x)-9) / (sd(x) / sqrt(25))
 
# out 1.751417
 
t
# out 2.06389
 
t,test(x,my=9)
# One sam test -> 
 

3 ways to test:

1. -m conf interval, check conf interval w/ null value. Null val in conf interval? 0? ! rejected
2. RAR, Tcalc
3. p-value; comapre w/ $\alpha$

y= rnorm(40,20,10)
t.test(y,mu=20)
 
qt(1-0.05 / 2, 40-1)
 
# is p value < .05 ? -> Reject null hyp! 
# 

Power

P(reject null hypothesis), formally: $1-\beta$, $\beta =$ prob of type of iterator

Example: