Here 1s the data from Jupyter for this discussion. Diameters data frame of the first sample (showing only the first five observations) diameters 0 267 1 3.08 2 22 i 2356 4 263 Diameters data frame of the second sample (showing only the first five chservations) diameters 0 243 1 162 2 338 30 056 4 289 test-statistic = -1.54 two tailed p-value =0.1229 Define the null and alternative hypotheses in mathematical terms as well as in words. Null hypothesis = H - p new prod = p existing prod Alternative = H: p new prod / p existing prod. Where p new prod, and p existing prod are the proportion of ball bearings with diameter less than 2. 20 cm in processes in both new and existing manufacturing processes H.: The null hypethesis will satisfy that the two proportions are equal for ball bearings with diameter less than 2.20 cm in both the new and existing manufacturing processes. H : The proportions are unequal for ball bearings with diameter less than 2.20 cm in new and existing processes. Identify the level of significance (0.03) Include the test statistic and the P-value. (test-statistic = -1.54) two tailed p-value = (0.1229) Provide a conclusion and interpretation of the test: Should the null hypothesis be rejected? Why or why not Since the p-value is greater than the significance level (0.1229=0.05), we fail to reject null hypothesis. We can therefore conclude at 5% level of significance that there is not sufficient evidence to conclude that the true population proportions are unequal from the new and existing processes. SE for the difference = SE + SE, observed difference - hypothesized difference test statistic = SE for the difference 1. Set the null and alternative hypotheses. Ho: H1 = M 2 Ha U1 M 2 (rich-tailed) Ho: HI # H2 (two-tailed) Where u ] and u , are means from distinct popolations In my conclusion I failed to reject the Null Hypothesis