Exam 8: Interval Estimation

If we want to find the required sample size for the interval estimation of the population proportion, and no reasonable estimate of this proportion is available, we assume the worst-case scenario under which = 0.5.

What is z_α/2 for a 95% confidence interval of the population mean?

The sampling distribution of the population proportion is based on a binomial distribution. What condition must be met to use the normal approximation for the confidence interval?

The GPA of accounting students in a university is known to be normally distributed. A random sample of 20 accounting students results in a mean of 2.92 and a standard deviation of 0.16. Construct the 95% confidence interval for the mean GPA of all accounting students at this university.

The main ingredient for developing a confidence interval is the sampling distribution of the underlying statistic.

The daily revenue from the sale of fried dough at a local street vendor in Boston is known to be normally distributed with a known standard deviation of $120. The revenue on each of the last 25 days is noted, and the average is computed as $550. Construct a 95% confidence interval for the population mean of the sale of fried dough by this vendor.

The mortgage foreclosure crisis that preceded the Great Recession impacted the U.S. economy in many ways, but it also impacted the foreclosure process itself as community activists better learned how to delay foreclosure and lenders became more wary of filing faulty documentation. Suppose the duration of the eight most recent foreclosures filed in the city of Boston (from the beginning of foreclosure proceedings to the filing of the foreclosure deed, transferring the property) has been 230 days, 420 days, 340 days, 367 days, 295 days, 314 days, 385 days, and 311 days. Assume the duration is normally distributed. Construct a 90% confidence interval for the mean duration of the foreclosure process in Boston.

We draw a random sample of size 25 from the normal population with variance 2.4. If the sample mean is 12.5, what is a 99% confidence interval for the population mean?

Each portion of the SAT exam is designed to be normally distributed such that it has a population standard deviation of 100 and a mean of 500. However, the mean has changed over the years as less selective schools began requiring the SAT, and because students later began to prepare more specifically for the exam. Construct a 90% confidence interval for the population mean from the following eight scores from the math portion, using the population standard deviation of 100: 450, 660, 760, 540, 420, 430, 640, and 580.

The National Center for Education would like to estimate the proportion of students who defaulted on their student loans for the state of Arizona. The total sample size needed to construct a 95% confidence interval for the proportion of student loans in default with a margin of error equal to 4% is ________.

The average natural gas bill for a random sample of 21 homes in 19810 zip code during the month of March was $311.90 with a sample standard deviation of $51.60. The 90% confidence interval around this sample mean is ________.