Question

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?

   Diameters data frame of the first sample (showing only the first five observations)
      diameters
   0       2.31
   1       2.48
   2       2.34
   3       1.89
   4       2.64
   
   Diameters data frame of the second sample (showing only the first five observations)
      diameters
   0       1.96
   1       2.68
   2       2.11
   3       2.21
   4       2.44

test-statistic = 0.0
two tailed p-value = 1.0

Answer 1

The hypothesis being tested is:

H0: p1 = p2

H0: The two proportions are the same

Ha: p1 ≠ p2

Ha: The two proportions are different

The level of significance is 0.05.

The p-value is 1.0.

Since the p-value (1.0) is greater than the significance level (0.05), we fail to reject the null hypothesis.

Therefore, we can conclude 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.