Exam 8: Interval Estimation

A large university is interested in the outcome of a course standardization process.They have learned that 150 students of the total 1,500 students failed to pass the course in the current semester.Construct a 99% confidence interval on the population proportion of students who failed to pass the course.Was the normality condition met for the validity of the confidence interval formula?

A sample of holiday shoppers is taken randomly from a local mall to determine the average daily spending on gifts.From a preselected sample,the standard deviation was determined to be $26.You would like to construct a 95% confidence interval for the mean daily spending on all holiday spending. A)Find the appropriate sample size necessary to achieve a margin of error of $5. B)Find the appropriate sample size necessary to achieve a margin of error of $8.

How is the consistency of estimators defined?

What is for a 90% confidence interval of the population mean?

The snowfall (in inches)during the month of January in a particular geographic region is normally distributed with a standard deviation of 16.75.In the last 12 years,the sample average of snowfall is computed as 122.50. A)Construct a 90% confidence interval of the average snowfall in this region. B)Construct a 95% confidence interval of the average snowfall in this region. C)Comment on the width of the preceding confidence intervals.

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.

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?

For a given confidence level and sample size n,the width of the confidence interval for the population mean is narrower,the greater the population standard deviation σ.

In order to estimate the mean earnings forecast for a large company,an investor looked up earnings forecasts from six financial analysts.The six forecasts he found were 200,220,300,185,210,and 210 (in millions).Suppose the investor knows the population standard deviation is 25 million.Calculate a 95% confidence interval of the population mean earnings forecast.

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 medical devices company wants to know the number of hours their 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 hours when calculating a 98% confidence interval?

Which of the following is the correct formula for the margin of error in the interval estimation of p?

The personnel department of a large corporation wants to estimate the family dental expenses of its employees to determine the feasibility of providing a dental insurance plan.A random sample of six employees reveals the following family dental expenses: $180,$260,$60,$40,$100,and $80.It is known that dental expenses follow a normal distribution.Construct a 90% confidence interval for the average family dental expenses for all employees of this corporation.

We draw a random sample of size 36 from a population with the standard deviation 3.5.If the sample mean is 27,what is a 95% confidence interval for the population mean?

A financial analyst would like to construct a 95% confidence interval for the mean earnings of a company.The company's earnings have a standard deviation of 12 million.What is the minimum sample size required by the analyst if he wants to restrict the margin of error to 2 million?

For a given confidence level and sample size,which of the following is true in the interval estimation of the population mean when σ is known?

What is the minimum sample size required to estimate a population mean with 95% confidence when the desired margin of error is D = 1.5? The population standard deviation is known to be 10.75.

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

For a given confidence level and population standard deviation σ,the width of the confidence interval for the population mean is wider,the smaller the sample size n.

Construct a 95% confidence interval on the population proportion for the support of candidate A in the following mayoral election.Candidate A is facing two opposing candidates in a mayoral election.In a recent poll of 300 residents,she has garnered 51% support.