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

A 2017 survey conducted by the National Science Foundation indicated that fewer than 15% of those currently employed in a STEM (Science, Technology, Engineering, and Mathematics) field in the United States of America are under the age of 30.  You conduct a similar survey to determine whether a lower proportion of STEM field workers in your state are under the age of 30.  After collecting a random sample of 500 STEM field workers in your state, you find that 67 are under the age of 30. 

(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.