Download Hypothesis Testing - Introduction to Statistics | STAT 1222 and more Study notes Statistics in PDF only on Docsity! Hypothesis Testing (Stat 1222. Professor: Dr. A. Biswas)
(1) Terminologies: Hy (read H-nanght) versus H,, (read H-alternative ); “is” means “equal to”, more
than/greater than: >, less than/smaller than: <, greater than or cqual to: >, less than or equal to:
<.
(2) Ho always contains statements of “equalities”, i.e., symbols like =, >, <. H, always contains statements
of “inequalities”, i.e., symbols like 4, >, <.
(3) Claim can be either Hp or H, depending on the statement of the problem.
(4) The type of test, ie., right-sided (or right-tailed), left-sided (or left-tailed) or two-sided (two-tailed) is
determined entirely by Hy.
Ai, contains >: right-tailed, H,, contains <: left-tailed, Hz, contains #: two-tailed.
(5) Level of significance (denoted by a): This is the maximum allowable probability of making Type I
error. This will be given in a problem.
(6) P-value: Assuming the null hypothesis is true, this is the probability of obtaining a sample statistic
“as extreme or more extreme” than the one determined from sample data.
(7) Area of rejection region always equals level of significance a.
Testing for population mean () at level a:
One-Sided Tesi for ys Two-Sided test for 4
Right tailed test Left tailed test
Null Hyp. Agi jesk Ho: p>k Ho: pak
vs. vs. vs. vs.
Alternative Hyp. Ha: p>k Ayipck Ay: pf#k
= = 7 F (nlarge, ¢ known) or z= WW (n large, ¢ unknown)
Test Statistic or
(a small, ¢ unknown, poplin. normal)
z< 2% 2 < —Z OF Z > Zo
Meir afte ens :
‘ oN Tk a“ N£ offy,
alll | a Waa
bs “2
rd E ° Fen.
Rejection Region (wets) or los - bey or for to}
t<to E< ty or t> to
Look in ¢ table with (mw — 1) df.
P-Value Area to the right
me,
of z | Area to the left of z 2(Area in the tail of z }
{only for n large) oad oo }
4
Ebsoree
z
Test using Rejection Region:
e Bvaluate the test statistic and check the condition specified by the Rejection Region.
® If the condition helds “Reject Hp at level a”
« If the condition dees not held “Do not reject Ho at level a”
Test using p- Value:
0 HP-Value <a, “Rejoct Ho at levela” ¢ If P-Value > a, “Do not reject Hp at level a”
