A machine shop which manufactures toggle levers has both a day and the night shift. A toggle lever is defective if a standard nut cannot be screwed onto the threads. Let p1 and p2 be the proportion of defective levers among those manufactured through the day as well as night shifts, respectively. We wish to test if there is the significant difference in the proportion of defective levers manufactured by two shifts.
a. Discuss your null as well as alternative hypotheses.
b. Describe your test statistic and discuss the critical region (rejection region) that has a = 0.05 significance level.
c. If samples of sizes??1=900 and??2=1000 and are taken from the two shifts correspondingly and y1 = 33 and y2 = 53 defectives were observed for the day and night shifts, compute the test statistic and state your conclusion.