Can you verify my answers/explanation (highlighted)? I was unsure of the math equation for the alternative hypothesis and is the p-value two-tailed or one-tailed needed for this comparison? Any help would be appreciated.

Discussion 4: -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. Diameter's data frame of the first sample (showing only the first five observations} diameters 2.79 2.13 2.35 2.15 1.82 thiIO Diameter's data frame of the second sample [showing only the first five observations} diameters 3.82 1.38 1.03 1.71 2.47 JthrIO 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? - Define the null and alternative hypotheses in mathematical terms as well as in words. Null hypothesis [Ho] there is no significant difference in the proportion of the ball bearings with a diameter less than 2.20 cm between the existing manufacturing process and the new manufacturing process. Alternative hypotheses {Hal there is a significant difference in the proportion of the ball bearings with a diameter less than 2.20 cm between the existing manufacturing process and the new manufacturing process. Ho = u: = to Alternative \"a = \"1' "2 h hypothesis: Should it teststatistic = 4.05 be not equal to? two tailed p-value = 0.28?6 Level of Significance = 0.05 Should the Null Hypothesis be rejected? Why or why not? The p-value 0.23105 is not less than the level of significance of 0.05. The null hypothesis should not be rejected. There is no sufcient evidence to conclude that there is a significant difference in the proportion of the ball bearings with a diameter of less than 2.20 cm between the existing manufacturing process and the new process