Exam 10: Introduction to Estimation

A financial consultant wanted to determine the mean annual return on Bond funds.A random sample of 60 returns shows a mean of 12%.If the population standard deviation is assumed to be 4%, estimate with 95% confidence the mean annual return on all Bond funds.

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

The sample proportion is a consistent estimator of the population proportion p because it is unbiased and the variance of is p(1- p) / n, which grows smaller as n grows larger.

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.

The sample size needed to estimate a population mean within 2 units with a 95% confidence when the population standard deviation equals 8 is

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

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.

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

The sample size needed to estimate a population mean to within 10 units was found to be 68.If the population standard deviation was 50, then the confidence level used was:

A confidence interval is a probability statement about the ____________________ mean.

Define relative efficiency.

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

Suppose a sample size of 5 has mean 9.60.If the population variance is 5 and the population is normally distributed, the lower limit for a 92% confidence interval is 7.85.

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

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

The sample variance is a point estimate of the population variance.

The problem with relying on a point estimate of a population parameter is that:

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.

How large a sample of federal employees in Nevada should be taken if we want to estimate with 98% confidence the mean salary to within $2,000.The population standard deviation is assumed to be $10,500.

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?