For the situation given in part (b) of Exercise 6.5.15, calculate the tests defined in Exercises 6.5.12 and 6.5.14. Obtain the approximate p-values of all three tests. Discuss the results.
Exercise 6.5.15
A machine shop that manufactures toggle levers has both a day and a 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 by the day and night shifts, respectively. We shall test the null hypothesis, H0 : p1 = p2, against a two-sided alternative hypothesis based on two random samples, each of 1000 levers taken from the production of the respective shifts. Use the test statistic Z∗ given in Example 6.5.3.
(a) Sketch a standard normal pdf illustrating the critical region having α = 0.05.
(b) If y1 = 37 and y2 = 53 defectives were observed for the day and night shifts, respectively, calculate the value of the test statistic and the approximate pvalue (note that this is a two-sided test). Locate the calculated test statistic on your figure in part (a) and state your conclusion. Obtain the approximate p-value of the test.
Example 6.5.3