Pls help me to do the following

Q)Carryout the following test using the binomial distribution where random variable X represents the number of successes.

H0:p= 0.50; H1:p¹ 0.05; n = 20, x = 7 and using a 10% level of significance.

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- Mar 6th 2009, 06:38 AMSashikalaHypothesis Test
Pls help me to do the following

Q)Carryout the following test using the binomial distribution where random variable X represents the number of successes.

H0:*p*= 0.50; H1:*p*¹ 0.05; n = 20, x = 7 and using a 10% level of significance. - Mar 6th 2009, 10:41 PMCaptainBlack
Suppose that $\displaystyle H0$ holds, then calculate the probability of getting a result outside the interval $\displaystyle np\pm 2$, with $\displaystyle p=0.5$. If this probability falls below $\displaystyle 0.1$ then you reject the null hypothesis at the $\displaystyle 10\%$ level of significance as the observed result is outside the given interval.

You calculate the probability using the binomial distribution:

$\displaystyle P(x \in (8,12))=\sum_{i=8}^{12} b(i,0.5,20)$

where $\displaystyle b(i,p,20)$ is the probability of exactly $\displaystyle i$ success in $\displaystyle n$ trials with probability of success on a single trial $\displaystyle p$ for the binomial distribution.

CB - Mar 7th 2009, 12:06 AMSashikalaHypothesis test
Thanks captain.

I figured it in the following way. Pls say whether this is alright.

Test static X has the binomial distribution which can be written as

X ~B(20,0.5)

This seems to be a two tailed test and since the value

of p given for H0 is 0.5, then the distribution of the test static X will be symmetrical.

From the table of binomial distribution

P(x<=7)=0.1316

So the probability for the two tailed test will be = 0.1316*2=0.2632

Hence we cannot reject H0 for the significance level of 10%.

Is this argument correct? Pls comment.