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# S2 two tailed tests? watch

1. I'm not entirely sure how to do these.

I can find the critical region fine, but how do I prove whether a test is significant?

for example

in the Heinemann book; 4C question 5.
Carry out the following test.

H0: p = 0.5
H1: p does not = 0.5

n=20, x=7
using a 10% level of significance

---

Ok, here's what I'm doing, can anyone point out my mistake?

X~B(20,0.5)

P(X<=7)= 0.1316
P(X>=7)= 1 - 0.9423

not significant.
The answer in the back is also not significant, but it says 0.2632!

what am I doing wrong?
2. You're doing a one-sided test. The test with critical region

X <= 7 or X >= 13

has significance level 2*0.1316.
3. (Original post by Jonny W)
You're doing a one-sided test. The test with critical region

X <= 7 or X >= 13

has significance level 2*0.1316.
where did X >= 13 come from?

I don't quite understand you.. what am I doing wrong?
4. (Original post by Jonny W)
You're doing a one-sided test. The test with critical region

X <= 7 or X >= 13

has significance level 2*0.1316.
why do you double it?
5. (Original post by kimoni)
where did X >= 13 come from?

I don't quite understand you.. what am I doing wrong?
One-sided test
H0: p = 0.5
H1: p < 0.5
You reject H0 when X <= 10 - k. The significance level is the value of P(X <= 10 - k) when p = 0.5.

Two-sided test
H0: p = 0.5
H1: p not equal 0.5
You reject H0 when X <= 10 - k or X >= 10 + k (ie, when |X - 10| >= k). The significance level is the value of P(X <= 10 - k or X >= 10 + k) when p = 0.5. The symmetry of the normal distribution about its mean implies that P(X <= 10 - k or X >= 10 + k) = 2P(X <= 10 - k). That's why your answer is wrong by a factor of 2.
6. (Original post by Jonny W)
One-sided test
H0: p = 0.5
H1: p < 0.5
You reject H0 when X <= 10 - k. The significance level is the value of P(X <= 10 - k) when p = 0.5.

Two-sided test
H0: p = 0.5
H1: p not equal 0.5
You reject H0 when X <= 10 - k or X >= 10 + k (ie, when |X - 10| >= k). The significance level is the value of P(X <= 10 - k or X >= 10 + k) when p = 0.5. The symmetry of the normal distribution about its mean implies that P(X <= 10 - k or X >= 10 + k) = 2P(X <= 10 - k). That's why your answer is wrong by a factor of 2.
OK... *deep breath*

so in simple terms, when I want to find the significance level of a two tailed test, I must always double my answer?
and is it always P(X<=x) and not P(X>=x)?
7. in simple terms with a two-tailed test (when the alternative hypothesis states that it doesn't equal mean/p) you half the significance level putting half at each end of the distribution and if the z-score (for normal) is more than the z-score of 1/2 the significance level then you reject the null hypothesis
8. (Original post by kimoni)
OK... *deep breath*

so in simple terms, when I want to find the significance level of a two tailed test, I must always double my answer?
and is it always P(X<=x) and not P(X>=x)?
Doubling always works, even if the distribution isn't symmetric (despite what I suggested in my previous post).

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