Discuss the below:
Confidence Intervals and One-Sample Hypothesis Test
1. Collect data. Develop a 90% confidence interval and a 95% confidence interval for the population mean. Did you use a z statistic or t statistic? Why? Compare the size and meaning of the two confidence intervals.
2. Take a random sample and test a hypothesis about a population mean. Explain what assumptions you made.
In a nutshell, the idea is to show that you understand confidence intervals and hypothesis testing and can interpret your results carefully. The checklist below provides details.
For this project, you may work alone or in a group of up to two other classmates. You may choose your own group members. One selection approach is to read the introductions conference and ask someone who has similar interests to join you. Note that email addresses are listed for everyone in the Class Members link at the left.
Here is a Project Checklist:
? Title
? Your Name(s) (Please include your name in your documents. For a group, include all names.)
? Area of Interest and Why the data are of interest to you (Brief explanation; Ex: What are your expectations, what questions/issues would you like to address?)
? Population and Variable (Define carefully)
? Data Source (Be specific; if you provide a link, that linked page should show the data, or it should be carefully explained how to locate the data)
? Sampling Method (Description)
? Data
? Sample Size (n)
? Sample Mean (can just state result; work not required)
? Sample Standard Deviation (can just state result; work not required)
? Standard Error of the Mean
? Type of statistic used (Z or t) and why
(Unless you know the population standard deviation or have a large sample size, you will want to use a t statistic)
? Confidence Intervals
? 90% confidence interval
? 95% confidence interval
(Please show calculations, indicating you understand how the confidence interval is determined. You are welcome to use PHStat2 to show a check of your answers.)
? Hypothesis Test [Make it clear what question you are trying to answer. The test could be one-tail or two-tail, depending on your question. ]
? Null Hypothesis
? Alternative Hypothesis
? Significance Level
? Critical value(s)
? Decision Rule (based on the critical value approach)
? Test Statistic
? Interpretation of Result of Hypothesis Test (based on the critical value approach)
? p-Value (using Excel) and interpretation of result of hypothesis test based on the p-value approach)
? Check of the Assumptions (Comment on the assumptions made -- pages 361 and 435 provide good guides to the situation where the population standard deviation is unkown.)
Normal Probability Plot, Box-and-Whisker Plot and/or Histogram (in checking the assumptions, provide at least one of these descriptive charts and comment on your results.)
? Summary (Summary and interpretation of results for the confidence intervals and hypothesis test)
Suggestions for Topics: There are many possible areas for study.
Devise an interesting hypothesis to test; for example, use a benchmark for the population mean, and carry out either a two-tailed or one-tailed test as appropriate. See the Sample Projects to get an idea how to arrive at a benchmark.
Some possibilities include:
Examination of prices for a particular commodity, such as houses, gas, milk, a company stock, etc
Weather data, such as temperature or rainfall.
Examples similar to those in the textbook and the course modules