This problem addresses testing a hypothesis for two population proportions. Here is the problem:
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.
Usually the null hypothesis is the two proportions are equal, but it appears the problem is defining that as the alternative hypothesis. If that were the case, what is the null hypothesis? If it's not the case, then what really is the alternative hypothesis? This is confusing. I appreciate all help.
The problem wants me to do a ztest by the way.