[7) 4. A factory currently uses a manufacturing protocol that results in products with a rejection proportion of 0.12 (12%). A new protocol has been proposed, and the goal is to determine whether the rate of rejected products will change from 0.12 to some other value under this new protocol. A sample of n = 395 products are collected following this new protocol, and 58 of them are rejected. The floor manager remarks that it is essential that the new protocol must not have a higher rejection rate than 0.12 (the old standard). [2] (a) Carry out a hypothesis test determining whether the proportion of rejects in the new process is different from 0.12. Use a significance threshold of a = 0.05. State all relevant hypotheses (in symbols) and test statistics/ distributions, as well as the p-value and appropriate conclusion of the test. You may use geogebra to help out with computations for this problem. Hint: You shouldn't end up rejecting the null hypothesis. [2] (b) Carry out a hypothesis test determining whether the proportion of rejects in the new process is greater than 0.12. Use a significance threshold of a = 0.05. State all relevant hypotheses (in symbols) and test statistics/distributions, as well as the p-value and appropriate conclusion of the test. You may use geogebra to help out with computations for this problem. Hint: You shouldn't end up rejecting the null hypothesis. [1] (c) Explain, in your own words, what possible advantages there could be to using a two-tailed test (part a), and what advantages there could be to a one-tailed test (part b). Which test would be more likely to report a statistically significant increase in the proportion of rejects? [2] (d) The floor manager is delighted that neither test achieved statistical significance, and declares they will switch to the new protocol. However, you can't help but be concerned by the results of the test you conducted in part b). Explain to the floor manager why the results from part b) are still somewhat alarming