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. 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. Given: (data below was calculated from Python) Diameters data frame of the first sample (showing only the first five observations out of 50) diameters 0 2.18 1 1.91 2 2.20 3 2.94 4 2.64 Diameters data frame of the second sample (showing only the first five observations out of 50) diameters 0 2.81 1 3.42 2 3.36 3 3.38 4 3.83 test-statistic = 0.42 and two tailed p-value = 0.6769 After analyzing the data, 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. (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?
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. 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.
Given: (data below was calculated from Python)
Diameters data frame of the first sample (showing only the first five observations out of 50)
diameters
0 2.18
1 1.91
2 2.20
3 2.94
4 2.64
Diameters data frame of the second sample (showing only the first five observations out of 50)
diameters
0 2.81
1 3.42
2 3.36
3 3.38
4 3.83
test-statistic = 0.42 and two tailed p-value = 0.6769
After analyzing the data, 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. (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?
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