S2 Hypothesis Testing - Significance level Watch

CalculusMan
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#1
Report Thread starter 12 years ago
#1
Carry out this test using a binomial distribution where the random variable X represents the number of successes:

H0: p = 0.50; H1: p =/= 0.50; n = 20, x = 7 and using a 10% level of significance.

So; X ~ Bin(20, 0.5)

I am looking for P(X > 7) + P(X < 7) or 1 - P(X = 7)

None of these give me the correct answer of 0.2632.

Am I going the right way about it?
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Kolya
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Hello!

You seem to be confused about exactly what the hypothesis test is doing. We have the null hypothesis and alternative hypothesis given. Now, our result to test whether or not these are true is n=20, x=7. A two-tailed hypothesis test means we multiply our result by two and then compare it to the sig level.

X ~ Bin(20,0.5)
n=20, x=7
P(x \leq 7) = 0.1316.

As it is two tailed:
2 x 0.1316 = 0.2632.

The result is not significant at level of 10%. H0 is still valid.

Hope this helps!
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Trangulor
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You shouldn't be getting 0.2632 as your final answer, it'll either be keep H0 or reject it.

In this case, since you clearly have a value lower than the expected mean, shouldn't H1 be p<0.50?

You need to work out P(X<=7). If that is less than your critical value (ie, is so unlikely to happen if your H0 is correct), then you reject H0
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Kolya
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(Original post by Trangulor)
In this case, since you clearly have a value lower than the expected mean, shouldn't H1 be p<0.50?
The fact that H1 is p\neq 0.5 tells us that it is a two-tailed test and therefore we must double the probability of our result before comparing it to the significance level. If it said p<0.5 then it would be a one-tailed test.
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khaixiang
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Just one question, my teacher is so adamant that we should instead halve the significant level then compare it with P(x \leq 7) = 0.1316 in this case.

I know it's essentially the same thing, but then I won't get the "correct" answer of 0.2632
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