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Chapter 8: Problem 52
What is the point estimator of the population proportion, \(p\) ?
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A researcher wants to determine a \(99 \%\) confidence interval for the mean number of hours that adults spend per week doing community service. How large a sample should the researcher select so that the estimate is within \(1.2\) hours of the population mean? Assume that the standard deviation for time spent per week doing community service by all adults is 3 hours.
a. Find the value of \(t\) for the \(t\) distribution with a sample size of 21 and area in the left tail equal to \(.10 .\) b. Find the value of \(t\) for the \(t\) distribution with a sample size of 14 and area in the right tail equal to \(.025 .\) c. Find the value of \(t\) for the \(t\) distribution with 45 degrees of freedom and \(.001\) area in the right tail. d. Find the value of \(t\) for the \(t\) distribution with 37 degrees of freedom and \(.005\) area in the left tail.
For a population data set, \(\sigma=14.50\). a. What should the sample size be for a \(98 \%\) confidence interval for \(\mu\) to have a margin of error of estimate equal to \(5.50\) ? b. What should the sample size be for a \(95 \%\) confidence interval for \(\mu\) to have a margin of error of estimate equal to \(4.25\) ?
A city planner wants to estimate the average monthly residential water usage in the city. He selected a random sample of 40 households from the city, which gave a mean water usage of \(3415.70\) gallons over a 1-month period. Based on earlier data, the population standard deviation of the monthly residential water usage in this city is \(389.60\) gallons. Make a \(95 \%\) confidence interval for the average monthly residential water usage for all households in this city.
You are working for a bank. The bank manager wants to know the mean waiting time for all customers who visit this bank. She has asked you to estimate this mean by taking a sample. Briefly explain how you will conduct this study. Collect data on the waiting times for 45 customers who visit a bank. Then estimate the population mean. Choose your own confidence level.
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