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Assume that out of 100 people chosen randomly in a survey in Portland 30% indicate that they vote democrat.

a) Estimate the proportion of people in Portland which vote Democrat. Give a 95% confidence interval for that proportion.

b.) Test on the 95%-level the hypothesis that there are more than 50% which vote democrat. Determine also the p-value.

Since I don't have the expectaction, variance or the standard deviation I am having trouble with parts a and b.

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    So, 30 is what I will use for my expectation which will provide me the variance and standard deviation needed to solve the confidence level?2012-10-23

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Let me explain. The best estimate for the proportion $p$ is $\hat p = x/N$. Now we need to somehow tell how close this is to the actual population proportion $p$. We use confidence intervals to estimate the population proportion, for example a 95% confidence interval. To calculate the confidence interval we use $\hat p \pm {z_{\alpha /2}}\sqrt {\frac{{\hat p\hat q}}{N}}$ where $\hat q$ is the usual $1 - \hat p$. In your question $\alpha = 0.05$ which is the probability of type I error. So your $z$-score should be about 1.96. Now you can find the lower and the upper bound. Then we usually finish with a conclusion: We are 95% that the proportion ... is between ...

Hope this help. If you have not seen this you need to speak with your professor or look through your notes.

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    It depends on your calculator and the $z$-table. Double check your calculations instead of asking me -- that way you will learn something.2012-10-24