Math 227 Project 2: Inferences On Two Population Parameters

Math 227 Project 2 Inferences on Two Population Parameters

In this project, you will draw inferences on comparing two population parameters: proportions, means, or standard deviations (or variances). You will describe a problem including a general claim made about comparing two population parameters, collect data, test hypotheses, and construct and interpret a confidence interval to determine whether the claim made about two population parameters can still be supported by the samples collected. You will, then, write a report on your findings including all the required components below and turn in by the stated due date according to the guidelines provided in this paper.

Paper For Above instruction

Understanding the Problem

Begin by selecting a parameter of your choice—proportion, mean, or standard deviation—for which a general claim has been made or can be made. Consider a specific question or hypothesis relevant to a topic of interest, and identify the two populations you want to compare. Describe the problem and include the general claim about these two populations. Identify whether your variables are categorical or numerical. Collect data from two relevant samples, ensuring each sample has at least 30 data values. Explain how you obtained your data and discuss whether the sampling was random. If random sampling was not possible, justify the limitations.

Analyzing the Data

Clarify which parameter is being compared and define the response variable. Determine if your samples are dependent or independent. Provide appropriate numerical measures (such as sample means, proportions, standard deviations) and graphical displays to analyze your data. Check whether the necessary conditions for hypothesis testing are satisfied based on the parameter being investigated, including sample size, normality, and independence assumptions. Use appropriate statistical distributions (z, Student’s t, F) to perform tests.

Perform hypothesis testing by defining null and alternative hypotheses with correct symbols. Use statistical software or tools such as StatCrunch to calculate the test statistic and P-value. Interpret the P-value in the context of your problem, explaining whether the sample results provide enough evidence to reject the null hypothesis. Decide whether the sample difference is statistically significant and whether the initial claim about the populations still holds based on your analysis.

Construct and interpret a 95% confidence interval for the difference between the two population parameters. List the steps involved in constructing the interval using StatCrunch and interpret whether the interval supports your hypothesis test findings.

Drawing Conclusions

Summarize what your analysis indicates regarding the comparison of the two population parameters. Determine if your data supports or refutes the initial claim. Explain whether the observed sample difference is likely due to sampling variability or reflects a true difference in the populations. Discuss how these findings could be practically applied if relevant.

Summary

Write a concise summary highlighting the main findings from your analysis and conclusions. Clearly articulate whether the initial claim about the two populations remains supported based on your hypothesis test and confidence interval results. Emphasize the implications of your findings in context.

References

  • Agresti, A., & Franklin, C. (2016). Statistical Methods for the Social Sciences. Pearson.
  • Devore, J. L. (2015). Probability and Statistics for Engineering and the Sciences. Cengage Learning.
  • Gravetter, F. J., & Wallnau, L. B. (2017). Statistics for Behavioral Sciences. Cengage Learning.
  • Lemeshow, S., & Hosmer, D. W. (2017). Applied Logistic Regression. John Wiley & Sons.
  • Newbold, P., Carlson, W. L., & Thorne, B. (2013). Statistics for Business and Economics. Pearson.
  • McDonald, J. H. (2014). Handbook of Biological Statistics. Sparky House Publishing.
  • Moore, D. S., McCabe, G. P., & Craig, B. A. (2012). Introduction to the Practice of Statistics. W. H. Freeman.
  • Ott, R. L., & Longnecker, M. (2015). An Introduction to Statistical Methods and Data Analysis. Cengage Learning.
  • Rumsey, D. J. (2016). Statistics For Dummies. Wiley Publishing.
  • Wilkinson, L., & Task Force on Statistical Inference. (2018). Statistical methods in psychology journals: Guidelines and explanations. American Psychologist, 73(9), 936–944.

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