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 One-sample Proportion t-test for Poverty Levels
Statistical Topic:
One-sample t-test of a proportion  can be used to determine if a sample proportion or percentage is similar to previous census or other large survey values.  Since the data set consists of a categorical or qualitative variable, a sample proportion is computed from survey counts which come for two types of responses (usually yes and no).  The number of data values for this type of analysis needed is considerable larger than for a data set of a continuous variable.  By using both confidence intervals and the five steps of hypothesis testing for a proportion, 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. 
Student Issue:
Poverty is a socioeconomic problem in all countries throughout the world.  We pride ourselves in the United States as trying to help those in poverty through various goverment problems.  Still even with these programs in place, poverty is a cruel way of life for many Americans. 
Data Sets:
A county wishes to monitor the poverty level of its constituents every five years looking for both trends and a comparison of percentages with prior years.  A random sample of 400 families in the county were selected and 70 families where living below the poverty level.  The researcher wishes to compare this sample with the percentage of families living below the poverty level with a previous census value.
Goal of Data Analysis Lab:
Using the data set shown above, answer the following research question:
     Is the proportion of families living in the county below the poverty level equal to 20% (a previous census value)?
Statistical Techniques:
  1. What type of variable is whether a family is living below the poverty level or not?  Define the population and sample for this research question.  What is the distribution and function that defines this population? 
  2. Compute the graphical and numerical data analysis for this sample data set.  What is the probability that more than 50 families are below the poverty level?
  3. Compute the 95% confidence interval for the proportion of families who live below the poverty level.  Using this interval answer this research question.
  4. Complete the five steps of hypothesis testing for the stated research question.
  5. Under what conditions can the results of your 95% confidence interval equal the same results as the five steps of hypothesis testing?
  6. Suppose it was noted that homeless families were not included in the current sample as they were in the previous census. Forty homeless families were added to the sample and all were found to be living below the poverty level.  Using these new results, complete the five steps of hypothesis testing.