Exam 10: Introduction to Estimation

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.

An unbiased estimator is ____________________ if its variance gets smaller as n gets larger.

NARRBEGIN: College Dean 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.NARREND -{College Dean Narrative} What sample size should be used?

The $z _ { \alpha / 2 }$ value for a 95% confidence interval estimate for a population mean $\mu$ is

When constructing confidence interval for a parameter, we generally set the confidence level 1 - $\alpha$ 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.

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?

Which of the following is not a part of the formula for constructing a confidence interval estimate of the population mean?

Other things being equal, the confidence interval for the mean will be wider for 99% confidence than for 95% confidence.

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

NARRBEGIN: Time Spent Playing Comput 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.NARREND -{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.

To estimate the mean of a normal population whose standard deviation is 6, with a bound on the error of estimation equal to 1.2 and confidence level 99% requires a sample size of at least:

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

If there are two unbiased estimators of a parameter, the one whose variance is smaller is said to be relatively efficient.

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

The confidence interval estimate of the population mean is constructed around the sample mean.

NARRBEGIN: College Dean 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.NARREND -{College Dean Narrative} What sample size should be used if using a 95% confidence level?

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

The width of a confidence interval estimate of the population mean increases when the:

Draw a sampling distribution of an unbiased estimator for $\mu$ .

Suppose an interval estimate for the population mean was 62.84 to 69.46. The population standard deviation was assumed to be 6.50, and a sample of 100 observations was used. The mean of the sample was: