Statistics homework
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chapter20720assignment.docx|
Confidence Intervals |
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In this project you will compute confidence intervals. In particular, you will compute confidence intervals for the same quantity measured at different times, and you will then compare these intervals. The subject is temperature and the patterns exhibited over several years.
Temperature patterns seen to be changing around the U.S. Winters seem shorter, summers seem hotter, and major storms seem more frequent. Let’s collect some data and look at what’s happening in your area.
Remember the Weather Underground? Their page of weather data can be found at http://www.wunderground.com/ .
Collect the Max. Temperature reading for each day in your home city or a city near you in
1. February and August of the most recent year containing both.
1. February and August two years previous
1. February and August 4 years previous
The Exercises will tell you how to proceed with the data.
The University of South Carolina Statistics Department Web site contains a number of Java Applets located at http://www.stat.sc.edu/~west/javahtml/ConfidenceInterval.html
Go to this site and locate the applet on confidence intervals. There is a description of what the applet is doing along with instructions on its use. Here’s a little more info.
The applet simulates the sampling of data. In particular, it draws a sample of size 5 from a normal distribution that has a mean of 0 and a standard deviation of 1. The applet then computes a confidence interval for the mean of the distribution using the confidence level 1 – (such as 0.95 or 95%) and graphs the interval as a vertical line.
For example, if based on the first sample of 5, the computed confidence interval is -1.127 < < 0.626 , and the vertical line
is drawn with the confidence interval endpoints represented by the values on the vertical axis. If the second sample of size 5 gives the confidence interval -0.488 < < 1.265 then a second vertical line is added to the graph
and so on. The applet shows you fifty such intervals at one time.
1. Compute 99% confidence intervals for the average daily maximum temperature in February for each of the three years in which you collected data. How do they compare?
2. Compute 99% confidence intervals for the average daily maximum temperature in August for each of the three years in which you collected data. How do they compare?
3. After repeatedly executing the USC confidence interval applet, you will notice intervals that do not contain 0. Since these are confidence intervals for the mean of the underlying population and we know that population has a mean of 0, should we expect all confidence intervals to contain 0? Explain.
4. For an alpha value of 0.05, use the confidence interval applet to estimate the probability that 0 will not be in a confidence interval. Summarize your work in detail. What is the theoretical probability?
