You are a boy, and your herghe is 176 H_{c} / mu >= 476
9.11.20
always with eguany (Ho)
Η mu < 176
PENTICE HO
H_{0} / mu = 426
[μετε
H_{4} = mu < 476
Choose significanes level (How sensitive your west): Re jaceren ngion -One-sided test (mu < 17epsilon)
176
alle we do not
[LT] overline X sim N(mu, sigma * 2/n)
Assume sigma ^ 2 = 5.05epsilon ^ 2 overline x = 178 = 178 n = 13
If H_{C} is true trus, then overline x sim N(176, 5.056/13)
Pick 1%
Derive one-sided rejector segion Start from standard normal disum butiaR -2.3261% Z 0 * 0.1 =-2.326
Standartized resporian region is (- ∞, - 2, 326)
Z c, c_{2} O
Non-Standart: - 2.326 = (x - 176)/(5.056/(sqrt(13))) Dara overline X = 170 172.7 176 178 x^ * =+ 76 + (- 2.326) * 5.056/(sqrt(13)) = X = 172.7 Dara deesin's fall in rejecnon
( - o * a_{3}(72, 7)
alpha = 13 Conclusion Becaux & does not fall in the rejection igion (-00, 172.7) we cannot refoet Ho.
2 Problem is actually Try 10 uncnourn esnimare it from your data.
when pop is
Normal
Ux 3- sample variance. Magic Χμ d of χμ
hos Student t-distribucion with n-1/ckgrees of freedom.
4n * 30 massable from some
Beromer 012208
Haur Baits
Dara
178
@Μο μ=176 Η μ>176.
S5.056
Signit level ly, one sided sest Assume Dist of pop. is Normal
t-spore has + Dill win n-1dgrees of firadom.
In our example
7-176
5.056
~t-Dist, with 12 Degreas Given (Killer) and x freedom.
-Dist n-12.
Rijection region: [2.684,00]
t001-2.681.
Non-Mandard: 2.681 = -176 5056
176450562.681 179.8 父今179.8.
Cannor reject Ho
Let's use 2-score instead 20.0 2.326.
Rejoct Null
+ 178. 179.8
Standard normal
176+5.056 2.326
179.26 VS 179.8.
13
Z-score is greater
Degreeset fredom #ohsurations-1
approximate with se
in becomes laye (12730)
Dassumes O=5"