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 $2\mathrm{.}20$ cm in the existing manufacturing process is the same as the proportion in the new process. At alpha$=0\mathrm{.}05,$ 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:

Define the null and alternative hypotheses in mathematical terms as well as in words.

Identify the level of significance.

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.$)$

Provide a conclusion and interpretation of the test: Should the null hypothesis be rejected? Why or why not?