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Hypothesis Testing for The Difference Between Two Population Parameters Discussion

Hypothesis Testing for The Difference Between Two Population Parameters Discussion

I’m working on a Mathematics question and need guidance to help me study.

Use the link in the Jupyter Notebook activity to access your Python script. Once you have made your calculations, complete this discussion. The script will output answers to the questions given below. You must attach your Python script output as an HTML file and respond to the questions below.

In this discussion, you will apply the statistical concepts and techniques covered in this week’s reading about hypothesis testing for the difference between two population proportions. In the previous week’s discussion, you studied a manufacturing process at a factory that produces ball bearings for automotive manufacturers. The factory wanted to estimate the average diameter of a particular type of ball bearing to ensure that it was being manufactured to the factory’s specifications.

Recently, the factory began a new production line that is more efficient than the existing production line. However, the factory still needs ball bearings to meet the same specifications. To compare the accuracy of the new process against the existing process, the factory decides to take two random samples of ball bearings. The first sample is of 50 randomly selected ball bearings from the existing production line, and the second sample is of 50 randomly selected ball bearings produced from the new production line. For each sample, the diameters of the ball bearings were measured.

The two samples will be generated using Python’s numpy module. These data sets will be unique to you, and therefore your answers will be unique as well. Run Step 1 in the Python script to generate your unique sample data.

Suppose that the factory claims that the proportion of ball bearings with diameter values less than 2.20 cm in the existing manufacturing process is the same as the proportion in the new process. At alpha=0.05, is there enough evidence that the two proportions are the same? Perform a hypothesis test for the difference between two population proportions to test this claim.

In your initial post, address the following items:

  1. Define the null and alternative hypotheses in mathematical terms as well as in words.
  2. Identify the level of significance.
  3. Include the test statistic and the P-value. See Step 2 in the Python script. (Note that Python methods return two tailed P-values. You must report the correct P-value based on the alternative hypothesis.)
  4. Provide a conclusion and interpretation of the test: Should the null hypothesis be rejected? Why or why not?

In your follow-up posts to other students, review your peers’ analyses and address the following questions:

  1. How does your conclusion compare to theirs?
  2. Do they have the correct conclusion based on their P-value and the level of significance? Why or why not?

Remember to attach your Python output and respond to all questions in your initial and follow up posts. Be sure to clearly communicate your ideas using appropriate terminology. Finally, be sure to review the Discussion Rubric to understand how you will be graded on this assignment.

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