Exam 10: Introduction to Estimation

The width of the confidence interval estimate of the population mean μ is a function of only two quantities: the population standard deviation σ and the sample size n.

The temperature readings for 20 fall days (degrees Fahrenheit)in Wheeling,West Virginia,are normally distributed with a mean of 5.5 degrees and a standard deviation of 1.5 degrees.Determine the 90% confidence interval estimate for the fall mean temperature.

Determine the sample size that is required to estimate a population mean to within 0.4 units with a 99% confidence when the population standard deviation is 1.75.

The librarian at the New York City Public Library has asked her assistant for an interval estimate of the mean number of books checked out each day.The assistant took a sample and found the mean to be 880 books.She provides the librarian with an interval estimate of between 790 and 970 books checked out per day.An efficient,unbiased point estimate of the number of books checked out each day at the New York City Public Library is:

Time Spent Playing Computer Games Suppose that the amount of time teenagers spend playing computer games per week is normally distributed with a standard deviation of 1.5 hours.A sample of 100 teenagers is selected at random,and the sample mean computed as 6.5 hours. ​ ​ -{Time Spent Playing Computer Games Narrative} Determine the 95% confidence interval estimate of the population mean if the sample size is changed to 36.

When constructing confidence interval for a parameter,we generally set the confidence level 1 − α close to 1 (usually between 0.90 and 0.99)because it is the probability that the interval includes the actual value of the population parameter.

Time Spent Playing Computer Games Suppose that the amount of time teenagers spend playing computer games per week is normally distributed with a standard deviation of 1.5 hours.A sample of 100 teenagers is selected at random,and the sample mean computed as 6.5 hours. ​ ​ -{Time Spent Playing Computer Games Narrative} Determine the 95% confidence interval estimate of the population mean if the sample size is changed to 300.

The confidence ____________________ is the chance that the interval contains the parameter,over repeated sampling.

A survey of 100 businesses revealed that the mean after-tax profit was $80,000.Assume the population standard deviation is $15,000: a.Determine the 95% confidence interval estimate of the mean after-tax profit for all businesses. b.Explain why you can use the confidence interval formula here,even though the population is not necessarily normal.

A random sample of 10 university students was surveyed to determine the amount of time spent weekly at the library.The times are: 13,14,5,6,8,10,7,12,15,and 3.If the times are normally distributed with a standard deviation of 5.2 hours,estimate with 90% confidence the mean weekly time at the library by all university students.

Time Spent Playing Computer Games Suppose that the amount of time teenagers spend playing computer games per week is normally distributed with a standard deviation of 1.5 hours.A sample of 100 teenagers is selected at random,and the sample mean computed as 6.5 hours. ​ ​ -{Time Spent Playing Computer Games Narrative} Determine the 95% confidence interval estimate of the population mean if the population standard deviation is changed to 1.2.

The sample variance s² is an unbiased estimator of the population variance σ² when the denominator of s² is n.

An engineer for an electric fencing company is interested in the mean length of wires being cut automatically by machine.The desired length of the wires is 12 feet.It is known that the standard deviation in the cutting length is 0.15 feet.Suppose the engineer decided to estimate the mean length to within 0.025 with 99% confidence.What sample size would be needed?

The error of estimation is the ____________________ between an estimator and the parameter.

In determining the sample size n needed to estimate the population mean,n decreases as the desired width of the confidence interval decreases.

It is ____________________ to say that a 95% confidence interval means there is a 95% chance that the parameter lies in that confidence interval.

In determining the sample size n needed to estimate the population mean,n is higher if the population standard deviation σ is higher.

College Dean A college dean would like to estimate a population mean to within 40 units with 99% confidence given that the population standard deviation is 200. ​ ​ -{College Dean Narrative} What sample size should be used?

The sample size needed to estimate a population mean to within 1 unit with 90% confidence given that the population standard deviation is 10 is 17.

We do not have control over the population standard deviation when forming a confidence interval,but we can control the ____________________ and the ____________________.