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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 Presidentâ€™s handling of the crisis in the financial markets. The results show that 575 out of the 1280 people polled say they either â€œapproveâ€ or â€œstrongly approveâ€ of the Presidentâ€™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 â€œapproveâ€ or â€œstrongly approveâ€ of the Presidentâ€™s handling of the crisis in the financial markets.
Now, hereâ€™s an interesting twist. If the same sample proportion was found in a sample twice as largeâ€”that is, 1150 out of 2560â€”how would this affect the confidence interval?