Using approximations to the binomial distribution

[bonfire09]

Homework Statement

This is the problem I am given.

. It is in he picture below or in the thumbnail. I was also told that since $n$ is big enough that I can use normal approximations.

Homework Equations

The Attempt at a Solution

I think that $C_{\alpha}=C_{0.1}=2.33$ which I got off the Z-score chart. The test statistic given looks like the one given for a binomial distribution given by where $Z=\dfrac{x-np}{\sqrt{npq}}=\dfrac{\frac{x}{n}-p}{\frac{\sqrt{pq}}{\sqrt{n}}}$. I am not sure if this right or not. But it seems like this is the only way of finding the critical value. Thanks[/B]

 

[RUber]

I think you looked up the value for alpha = .01, you were asked for .1. If you are using a normal approximation, then this is all you need to find the critical value. Be sure to clarify if this is a one-tailed or two-tailed test. From the question T>C_alpha indicates you are checking to see if a majority are in favor--i.e. one-tailed, your process is correct. If you were just checking whether or not the null hypothesis held, you would use a two-tailed test. In that case, you would need to divide alpha by two.

 

[bonfire09]

I see it is two tailed so I would use $C=1.645$ which would be my critical value.

 

[RUber]

Right--In this case the two tailed test is for p = 50%, if you reject that, then you know it is either more or less. If you were only concerned with the proportion being more, then you could use a smaller critical value to get the same level of confidence.