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 One-sample Mean t-test for Radon Effect on Cancer
Statistical Topic:
One-sample t-tests can used to determine if a sample mean complies with certain population mean such as EPA clean air mandated values on various pollutants or safe levels of chemicals in the home environment.  This test is usually the first type of inferential test students learn how to conduct in an introductory statistics course.  By using both confidence intervals and the five steps of hypothesis testing, research questions can be proposed and answered with a high level of confidence and a minimum of error assuming correct sample data collection procedures were followed.  Data description is also important in hypothesis testing as it is these computed statistics and graphs that give us a hint of what the population distribution might look like and point estimates for population parameters.
Student Issue:
Exposure to various chemicals in our home can lead to health risks such as cancer and leukemia.  Some past research has shown that high indoor radon concentrations can lead to the development of cancer in both adults and children.
Data Sets:
The data set shown below presents radon concentrations (Bq/m^3) from homes in which a child was diagnosed with cancer.
   10   21   57   23   15    11     9   13   27   13   39   22
     7   20   45   12   15    38     8   11   18   16   23   16
   34   10   15   11   18  110   22   11     6   17   33   10
Goal of Data Analysis Lab:
Using the data set shown above, answer the following research question:
     Is the mean radon concentration in homes of children diagnosed with cancer higher than the national mean 
        average of 14.8 Bq/m^3?
Statistical Techniques:
  1. What type of variable is radon concentrations?  What are the two types of data analysis that can be completed on this sample data set?
  2. Complete both types of analyses for this data set.  Make sure to compute statistics that measure middle, spread, shape and outliers.  Make comments on any unusual findings.
  3. Compute a 95% confidence interval for the mean radon concentrations.  Using this interval, answer the research question.  
  4. Complete the five steps of hypothesis testing for the research question.
  5. Define alpha, beta and your p-value in terms of this data set.
  6. The radon value of 110 Bq/m^3 was found to be a typographical error.  The correct value was 10 Bq/m^3.  Redo the five steps of hypothesis testing.
Statistical Techniques:
  1. How is radon produced and is it always harmful?
  2. Can you suggest other chemical pollutants found in your home which might cause cancer?