Exam 9: Estimation and Confidence Intervals

The Central Limit Theorem proves that the sampling distribution of sample means tends to approximate a normal distribution when the sample size becomes larger.

We can expect a difference between a sample statistic and the corresponding population parameter.This difference is called the sampling error.

What is the interval within which a population parameter is expected to lie? __________________

A survey of 50 retail stores revealed that the average price of a microwave was $375 with a standard error of $20.If 90% and 95% confidence intervals were developed to estimate the true cost of the microwave,what similarities would they have?

A survey of an urban university (population of 25,450)showed that 870 of 1100 students sampled supported a fee increase to fund improvements to the student recreation center.Using the 99% level of confidence,what is the confidence interval for the proportion of students supporting the fee increase?

The mean weight of trucks traveling on a particular section of I-475 is not known.A state highway inspector needs an estimate of the mean.He selects a random sample of 49 trucks passing the weighing station and finds the mean weight is 15.8 tons.The population standard deviation is 3.8 tons.What is the 95 percent interval for the population mean?

An interval estimate is a range of values used to estimate a population parameter.

A point estimate is a single value used to estimate a population parameter.

A 95 percent confidence interval implies that about 95 out of 100 similarly constructed intervals will include the _____________ being estimated.

What happens to the computed value of t as the sample size increases? ______________

What does the t distribution approach as the sample size increases? ______________________

What is the measure that an interval estimate includes the population parameter? _____________________

Recently,a university surveyed recent graduates of the English Department for their starting salaries.Four hundred graduates returned the survey.The average salary was $25,000 with a standard deviation of $2,500.What is the 95% confidence interval for the mean salary of all graduates from the English Department?

All t distributions have a mean of zero and a standard deviation of 1.

A survey of 50 retail stores revealed that the average price of a microwave was $375 with a standard error of $20.Assuming the population is normally distributed,what is the 95% confidence interval to estimate the true cost of the microwave?

A confidence interval for a population mean

The t distribution is similar to the z distribution in all BUT one of the following characteristics.Which one is it?

Other things being equal,a smaller sample size would result in a wider confidence interval because the standard error of the mean is _______________.

One factor in determining the size of a sample is the degree of confidence selected.This is usually 0.95 or 0.99,but it may be any degree of confidence you specify.

One factor in determining the size of a sample is the maximum allowable error that you must decide on.It is the maximum error you will tolerate at a specified level of confidence.