IMPORTANT S2 question!! on Hypothesis Testing

using the following question as an example...
find the critical region:
H0: p = 0.20
H1: p ≠ 0.20
Two-tailed test with 0.05 significance level.

If H0 is true: X~B(25,0.20)

so, P(X«C1) ≈ 0.025
now from the table
P(X«0)= 0.0038
P(X«1)= 0.0274

which one of the above critical values do you use and why? is it the value closest to 0.025??????? :confused:

P(X»C2) ≈ 0.025
1 - P(X«C2-1) ≈ 0.025
P(X«C2-1) ≈ 0.975

P(X«8) = 0.9532
P(X«9) = 0.9827 (from tables)

same issue here, which value do i chose and why? any thing to do with the inequalities or is it just because its closer to 0.975.

Exam in a few hours!!! help me :confused:

Reply 1

confused?

1

i think its the one less than your significance level. to find critical region the prob should be less than 0.025 i think.

Reply 2

Sparkling_Jules

1

I know I did one question where it specifically asked for you to use the closest values but I don't know it that applies to every question.

Reply 3

confused?

1

so answers are

1. P(X«0)

2. P(X«8)

Reply 4

mctcdc0710

1

If it does not clearly state that u must use the value closer to 2.5 % or anything equivalent then u should use the value giving a probability smaller than 0.025 at both sides.

Now, if the exercise does state "as close as possible to 2.5% at each end" then you must compare 2 values. One giving probability more than 2.5% and the other less. let the first be p1 and the second p2, then u pick the one that |px-0.025| is less than the other.

Reply 5

KingAS

OP

confused?

i think its the one less than your significance level. to find critical region the prob should be less than 0.025 i think.

i think the answer says the opposite though?

P(X«1) is used and not P(X«0)

any one else?

Reply 6

RobbieC

15

It varies... Most of the time it is the one CLOSEST to the significance level of the tail. Over times, it MUST be within limits they give you.

Damn, I am still a little shaky with sorting out critical regions, I always get the inequalities wrong by about 1 :frown:

Reply 7

confused?

1

hes trying to find the rejection region which is x«0 and x«8. you dont use the closest one here.

Reply 8

KingAS

OP

ok, lemme try another one of those questions and ill see if i am getting the hang of it... if not i'll be back. give me 5mins!

Reply 9

mctcdc0710

1

so my post ment nothing for u guys ? Ok who cares go drown yourselves :biggrin:

Reply 10

Sparkling_Jules

1

Just skimming through my text book, they seem to use the one less than 0.025 unless asked otherwise.

Reply 11

hajira

drawing a sketch bar graph for the values of X helps
in first case
P(X«C1) ≈ 0.025
P(X«0)= 0.0038
P(X«1)= 0.0274
u shud b able to see that only part of the bar for x=1 is included
as this is a discrete distribuition, u cant hav part of a value of X
so C1=0

for the second bit
P(X«C2-1) ≈ 0.975
P(X«8) = 0.9532
P(X«9) = 0.9827

i think its helpful if u write it as
P(X»9) = 1-P(X«8)=0.0468
P(X»10) = 1-P(X«9)=0.0173
in this case again, sketch a bar graph n consider the amount of probability after the discrete value and compare it to 0.025, u can see that only part of bar for X=9 is included..

so C2=10

n CR is X«0 or X»10

p.bmp161.3KB

Reply 12

Faiz

sounds like drawing a graph will definitely help. hopefully it wont come up though...fingers crossed

Reply 13

hajira

Here's a question if anyone wants to test themselves :p:

From past records a manufacturer of glass vases knows that 15% of the production have slight defects. To monitor the production, a random sample of 20 vases is checked each day and the number of vases with slight defects is recorded.
(a) Using a 5% significance level, find the critical regions for a two-tailed test of the hypothesis that the probability of a vase with slight defects is 0.15. The probability of rejecting, in either tail, should be as close as possible to 2.5%. (5 marks)
(b) State the actual significance level of the test described in part (a). (1 mark)

if u want to confirm the answers, please post n i'll post them :smile:

Reply 14

confused?

1

hajira

Here's a question if anyone wants to test themselves :p:

From past records a manufacturer of glass vases knows that 15% of the production have slight defects. To monitor the production, a random sample of 20 vases is checked each day and the number of vases with slight defects is recorded.
(a) Using a 5% significance level, find the critical regions for a two-tailed test of the hypothesis that the probability of a vase with slight defects is 0.15. The probability of rejecting, in either tail, should be as close as possible to 2.5%. (5 marks)
(b) State the actual significance level of the test described in part (a). (1 mark)

if u want to confirm the answers, please post n i'll post them :smile:

is one of them x»6 ?