Re: Simple binomial test question

Hi, very simple I know, but just want to check that I
think correctly.


the problem:
"A coin is tossed 10 times and 2 heads are obtained.
Test Weather the coin
is biased."



So Definitely we are using binomial distribution,
isnt it? so

null hypothesis: "We get 5 heads"

alternative hypothesis: "head number<>5"




The null and alternative hypotheses have to be expressed in terms of the unknown probability of a head, p, and not the sample statistics. Thus,

H: p = 0.5 is tested against K: p not equal to 0.5.

The wording of the question suggests that the alternative hypothesis should be two-sided.




So its gonna be 2-tailed test. So if I calculate
propabilities to get 0,1,2
and add them I get the test value (which is about
0.054). But using 2-tailed
95% confidence level test, the first tail is located
at 0.025 and the right
tail is at 0.975. Becouse 0.054 is more than 0.025 ,
the null hypothesis
remains, so we cannot say that the coin is biased.




The specified type I error is called the significance level, not the confidence level. You may set significance level at 0.05. Since your calculated p-value of 0.054 exceeds the pre-asssigned significance level, you accept the null hypothesis H.

Intuitively you had the right idea, but you used the wrong terminology.

Jack




Did it go ok?? this is how my common sense says it
could be done. We cannot
use poison/normal distributions, couse sample size is
small, isnt it?? We do
2-tailed or one tailed? I am sure 2-tailed, just
checking ...



thanks


.

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