Statistics 226
Supplemental Instruction
Iowa State University / Leader: / Luyun
Course: / Stat 226
Instructor: / Anna Peterson
Date: / 3/6/16
The two properties of a high level confidence and but a narrow (precise) CI obviously work against each other.
The ______the level of confidence the ______the confidence interval and therefore the ______precision we have estimating the unknown population mean.
If we need a certain level of confidence, but also a specific precision, we can ______the sample size n.
· If the sample size n goes up:
· ______the standard error will decrease the overall width of the confidence interval.
Margin of error:
Changing one of the three components ______, ______, ______in the margin of error will have the different impacts on the overall width of a confidence interval.
· Changing level of confidence C:
· Changing sample size n:
· Changing σ:
Interpretation of confidence interval:
·
Be careful:
Before we take a sample from a population we can say there is C% chance, that our confidence interval will include the population parameter µ if we plan on constructing C% confidence interval.
______, this decision is made. Our interval either does contain µ or it does not. We just don’t know it. There is not a C% chance anymore; all we can say is that we are C% confidence.
True or False:
_____For a given standard error, lower confidence levels produce wider confidence intervals.
_____If you increase sample size, the width of confidence intervals will increase.
_____The statement, "the 95% confidence interval for the population mean is (350, 400)", is equivalent to the statement, "there is a 95% probability that the population mean is between 350 and 400".
_____ To reduce the width of a confidence interval by a factor of two (i.e., in half), you have to quadruple the sample size.
_____The statement, "the 95% confidence interval for the population mean is (350, 400)" means that 95% of the population values are between 350 and 400.
A random sample of 30 students are selected from an accounting masters program and information about the average number of hours per week they spend preparing for their CPA examination is collected. The sample yielded an average of 22 hours per week. Assume the population distribution is normal and the standard deviation is known to be 2 hours. Answer the following questions:
What is the sample size?
What is the sample mean?
What is the standard error of the sampling distribution?
Calculate a 90% confidence interval for the unknown population mean. Provide an interpretation in the context of this problem.
Calculate a 95% confidence interval for the unknown population mean. Provide an interpretation in the context of this problem?
Why are the interpretations of these confidence intervals in terms of the unknown population mean and not the sample mean?
Which of the two confidence intervals is wider? Is this what you would expect?
What would happen to the 90% confidence interval if we increased the sampling size to 100 masters of accounting students?
What are the necessary assumptions for constructing this confidence interval?