6 questions in math statistics. Must show all work for each. 

1.Political polls typically sample randomly from the U.S population to investigate the percentage of voters who favor some candidate or issue. The number of people polled is usually on the order of 1000. Suppose that one such poll asks voters how they feel about the President's handling of the crisis in the financial markets. The results show that 575 out of the 1280 people polled say they either "approve" or "strongly approve" of the President's handling of this matter. Based on the sample referenced above, find a 95% confidence interval estimate for the proportion of the entire voter population who "approve" or "strongly approve" of the President's handling of the crisis in the financial markets.
Now, here's an interesting twist. If the same sample proportion was found in a sample twice as large-that is, 1150 out of 2560-how would this affect the confidence interval? 

2.How is the rejection region defined and how is that related to the z-score and the p value? When do you reject or fail to reject the null hypothesis? Why do you think statisticians are asked to complete hypothesis testing? Can you think of examples in courts, in medicine, or in your area?

3.What is the difference between the 'null hypothesis' and the 'alternate hypothesis'?  

4.What are some tips for knowing 'how' to set up the two hypothesis?  

5.Is the 'claim' always the alternate hypothesis?  

6.When do we use a z-value rejection region when testing a claim about a population mean?  When do we use a t-value?