Write out the null and alternative hypotheses in words and symbols.  Identify the sample size and label it using the appropriate symbol.

The Center for Disease Control (CDC) determined that the average life expectancy for the U.S. population in 2018 was 78.7 years with a standard deviation of 6.5 years.  After learning this you decide to collect data from a random sample of Dutchess County obituaries from 2018-2020 to compare the life expectancy of Dutchess County residents to all United States citizens to determine whether Dutchess residents tend to live longer, or shorter lives compared to the national average.  A random sample of 51 local obituaries found an average age at the time of death of 75.6 years with a standard deviation of 10.3 years.   The sample data was approximately normally distributed.

(a) Write out the null and alternative hypotheses in words and symbols.  Identify the sample size and label it using the appropriate symbol.

(b) Determine whether it would be appropriate to use a theoretical approach to conduct a statistical analysis. 

(c)Use the appropriate applet to generate a distribution of simulated sample statistics.

     i.  If the criteria have been met to use the Theory-Based Inference applet.

     ii.  If the criteria have not been met to use the theoretical approach, explain how.  Using the One Proportion or the One Variable with Sampling applet and compare and contrast your simulated distribution with the normal distribution by using the “Normal Approximation” or “Overlay Normal Distribution” settings.  Use complete sentences.

    iii.  Include a screenshot of the applet, distribution, and p-value found.

(d)  Determine the appropriate formula (based on your variable type and approach) to calculate the standardized statistic.  Write the formula symbolically, then show the calculation by substituting in the appropriate values, simplifying the expression using the appropriate order of operations, then round your answer to 3 decimals. (e) Write a conclusion using complete sentences interpreting the p-value in the context of the research question.