What have I done wrong (Hypothesis Testing S2) Watch

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bbcer
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#1
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Can anyone tell me where I've gone wrong here please:

'A coin is tossed 20 times and a head is obtained on 6 occasions. Is there evidence to suggest that the coin is biased? Use a 5% two-tailed significance test'

Here's how I've answered it:

H0: p = 0.5
H1: p ≠ 0.5

If H0 is true, X ~ B(20, 0.5).

If the null hypothesis is true,
P(X ≥ 6) = 1 - P(X < 6) = 1 - P(X ≤ 5) = 1 - 0.0207 = 0.9793
Therefore it is not significant so the coin is not biased.

The answer at the back says it's not biased too but the probably they've worked out is 0.1154, not 0.9793 - have I done something wrong or is the answer at the back is wrong?

Also another question, which I can't answer:

Carry out the following test using the binomial distribution where the random variable X respresents the number of successes:
H0: p = 0.5
H1: p ≠0.5
n = 20
x = 7
(using a 10% level of significance)

Please help!
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drw25
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#2
Report 13 years ago
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Hmm...shouldn't you be working out the probability that it's less than equal to 6? If the coin were biased, you'd get less heads, not more.

And I think the second question's the same - except use 7 instead of 6.

Hope this helps.
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bbcer
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Report Thread starter 13 years ago
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(Original post by drw25)
Hmm...shouldn't you be working out the probability that it's less than equal to 6? If the coin were biased, you'd get less heads, not more.
You've got a point there but that will give me an answer of 0.0577 (from looking up the tables) not 0.1154, which is the book's answer.

(Original post by drw25)
And I think the second question's the same - except use 7 instead of 6.
I've tried answering the question the same way as I have done for the first one but I ended up with the wrong answer.
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drw25
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Report 13 years ago
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0.0577 is, bizarrely, half of the right answer, though. I'm not quite sure why...maybe the two-tailedness comes into play?
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Vijay1
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(Original post by drw25)
0.0577 is, bizarrely, half of the right answer, though. I'm not quite sure why...maybe the two-tailedness comes into play?
Yes, this is a two-tailed test if you say H1: p≠0.5,
so you would have to divide it, and consider both ends of the binomial distribution and then look it up in the tables for two-tailed test
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bbcer
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#6
Report Thread starter 13 years ago
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I still don't quite understand it. Can someone show me how to do the second question please.
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