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Exam 8: Interval Estimation

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Question 41

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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?

A) n ≥ 30
B)
C)
D)

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Question 42

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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.

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[114.55459,130.4541]...

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Question 43

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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.

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 for a 90% confidence interval of the population mean?

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.

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 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?

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?

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.

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.

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.

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.

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

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.

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?

How is the consistency of estimators defined?

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.

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

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 _____________________.