Exam 8: Interval Estimation

What is the most typical form of a calculated confidence interval?

A sample of 1,400 American households was asked if they planned to buy a new car next year.Of the respondents,34% indicated they planned to buy a new car next year.Construct a 98% confidence interval of the proportion of American households who expect to buy a new car next year.

For a given confidence level and population standard deviation,which of the following is true in the interval estimation of the population mean?

What is for a 95% confidence interval of the population mean based on a sample of 15 observations?

A sample of holiday shoppers is taken randomly from a local mall.Forty-nine shoppers were selected and asked what their average spending on gifts would be during the entire holiday season.The point estimate of the population mean was calculated as $550 and the sample standard deviation was calculated as $92.a.Construct a 95% confidence interval of the population mean spending.b.Explain how the central limit theorem is used in constructing this interval.

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.A 95% confidence interval is constructed for the population mean revenue.If the data from the last 40 days had been used,then the resulting 95% confidence intervals would have been _____________________.

A confidence interval is generally associated with a(n)_____________.

The minimum sample size n required to estimate a population mean with 95% confidence and the assumed estimate of the population standard deviation 6.5 was found to be 124.Which of the following is the approximate value of the assumed desired margin of error?

A 90% confidence interval is constructed for the population mean.If a 95% confidence interval had been constructed instead (everything else remaining the same),the width of the interval would have been ________ and the probability of making an error would have been _________.

A politician wants to estimate the percentage of people who like his new slogan.Given that no prior estimate of the population proportion is available,what is the minimum sample size such that the margin of error is no more than 0.08 for a 95% confidence interval?

For a given sample size and population standard deviation,which of the following is true in the interval estimation of the population mean?

Excel does not have a special function that allows to calculate t values.

A large earthquake hit a city in South America.A survey of 2,000 houses found that 600 of them had collapsed.Construct a 95% confidence interval for the proportion of collapsed houses.

A large university is interested in the outcome of a course standardization process.They have taken a random sample of 100 student grades,across all instructors.The grades represent the proportion of problems answered correctly on a midterm exam.The sample proportion correct was calculated as 0.78. a.Construct a 90% confidence interval on the population proportion of correctly answered problems. b.Construct a 95% confidence interval on the population proportion of correctly answered problems.

A medical devices company wants to know the number of hours its MRI machines are used per day.A previous study found a standard deviation of four hours.How many MRI machines must the company find data for in order to have a margin of error of at most 0.5 hour when calculating a 98% confidence interval?

A job candidate with an offer from a prominent investment bank wanted to estimate how many hours she would have to work per week during her first year at the bank.She took a sample of six first-year analysts,asking how many hours they worked in the last week.Construct a 95% confidence interval with her results: 64,82,74,73,78,and 87 hours.

If a small segment of the population is sampled then an estimate will be less precise.

The ages of MBA students at a university are normally distributed with a known population variance of 10.24.Suppose you are asked to construct a 95% confidence interval for the population mean age if the mean of a sample of 36 students is 26.5 years.What is the margin of error for a 95% confidence interval for the population mean?

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.

The t distribution table lists t_{df values for selected lower-tail probabilities and degrees of freedom df. FALSE}