Statistics problems Essay
Based on a simple random sample of one hundred an analyst estimates the average hourly wage earned by workers in a city to be $30 and computes the margin of error to be $5. Can we conclude from this that most workers there earn between $25 and $35 per hour? Is the right interpretation for the margin of error?
Polls showed the two main candidates in the 2004 presidential election were nearly tied on the day before the election. To predict the winner a newspaper would like to have a poll that has margin of error of less than 1%. Roughly how large a sample would be needed for such a poll? Chapter 8
6. A large population of overdue bills ha balances that follow a normal curve. When we take a sample of 100 of these the average is $500 and the SD is $100. (a) What statement can you make about the range $300 to $700? (b) What statement can you make about the range $480 to $520? 10. Pollsters try to determine whether or not a person is a “likely voter” before they count their opinion in a poll. If we assume 40% of the registered voters will actually vote, in a random sample of 100 registered voters we can be 95% confident that somewhere between ______ and ________ of them will actually vote.
Fill in the blanks with numbers. 22. An investment firm with 10,000 clients would like to accurately forecast the average dollar amount their current customers will deposit over the coming year. They decide to telephone a random selection of 25 of their customers to ask how much they plan to deposit, and they would like to keep this sample as small as possible so the calls do not annoy too many customers. Since they will be multiplying his average by the total number of customers to get an overall forecast, they would like to accurately estimate this average with a margin of error of less than $4,000. Last year, the average deposit for all 10,000 clients was $25,000 with a standard deviation of $30,000
Do you think a sample of 25 is enough to give them the margin of error they want? If not, how large a sample do you suggest they need to take? Justify you answer with relevant calculations.