Exam 10: Introduction to Estimation

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. -An electronics retailer is interested in studying the incomes of consumers in a particular area.The population standard deviation is known to be $1,000.What sample size would the researcher need to use for a 95% confidence interval if the difference between UCL and LCL should not be more than $100?

____________________ estimators do not have the capacity to reflect the effects of larger sample sizes.

In the formula ,the $\alpha$ / 2 refers to:

If you increase the confidence level,the confidence interval becomes ____________________.

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.

If the population standard deviation is guesstimated,and it turned out to be smaller than you assumed,then the sample size you calculated is ____________________ than it needs to be.

The sample variance s² is an unbiased estimator of the population variance $\sigma$ ² when the denominator of s² is n.

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 population standard deviation is changed to 1.2.

Suppose that a 95% confidence interval for $\mu$ is given by $\bar { x } \pm 3.25$ .This notation means that,if we repeatedly draw samples of the same size from the same population,95% of the values of $\bar { x }$ will be such that $\mu$ would lie somewhere between $\bar { x } - 3.25$ and $\bar { x } + 3.25$ .

The sample ____________________ is an unbiased estimator for the population mean.

When determining the required sample size for a confidence interval,you need to know the population ____________________,the confidence ____________________,and the ____________________ on the error of estimation.

As the bound on the error of estimation decreases,the sample size ____________________.

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. -A research firm has been contracted to estimate the mean weekly family expenditure on clothes.He believes that the standard deviation of the weekly expenditure is $125.Determine with 99% confidence the number of families that must be sampled to estimate the mean weekly family expenditure on clothes to within $15.

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.

Which of the following statements is correct?

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

A(n)____________________ estimator of a population parameter is an estimator whose expected value is equal to that parameter.

The term 1 - $\alpha$ refers to the probability that a confidence interval does not contain the population parameter.

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