Exam 10: Introduction to Estimation

Draw a sampling distribution of a biased estimator for $\mu$ .

A 95% confidence interval estimate for a population mean $\mu$ is determined to be 75 to 85.If the confidence level is reduced to 80%,the confidence interval for $\mu$ becomes wider.

An unbiased estimator is said to be consistent if the difference between the estimator and the parameter grows larger as the sample size grows larger.

Conference Rooms Rented A hotel chain wants to estimate the average number of conference rooms rented daily in each month.The population of conference rooms rented daily is assumed to be normally distributed for each with a standard deviation of 24 rooms. -{Conference Rooms Rented Narrative} During January,a sample of 16 days has a sample mean of 48 rooms.This information is used to calculate an interval estimate for the population mean to be from 40 to 56 rooms.What is the level of confidence of this interval?

We cannot interpret the confidence interval estimate of $\mu$ as a probability statement about $\mu$ because the population mean is a fixed quantity.

In determining the size n needed to estimate the population mean,n increases as the confidence level decreases.

Which of the following is a characteristic for a good estimator?

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.

Increasing the sample size fourfold decreases the width of the confidence interval by ____________________.

The term 1 - $\alpha$ refers to:

The width of a 95% confidence interval is 0.95.

An unbiased estimator has an average value (across all samples)equal to 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 mean is changed to 8.5 hours.

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 and interpret the 90% confidence interval estimate of the population mean.

If there are two unbiased estimators of a population parameter available,the one that has the smallest variance is said to be:

Given a mean of 2.1 and a standard deviation of 0.7,a 90% confidence interval will be 2.1 $\pm$ 0.7.

Because n is an integer and we want the bound on the error of estimation to be no more than a given amount,any non-integer value found for n must always be rounded ____________________.

Draw sampling distributions of a consistent estimator for $\mu$ where one sample mean is larger than the other.

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 if using a 95% confidence level?

The value for a 95% confidence interval estimate for a population mean $\mu$ is