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A machine shop that manufactures toggle levers has both a day and a night shift. A
Chapter 8, Problem 8.3-11(choose chapter or problem)
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. (a) Define the test statistic and a critical region that has an = 0.05 significance level. Sketch a standard normal pdf illustrating this critical region. (b) If y1 = 37 and y2 = 53 defectives were observed for the day and night shifts, respectively, calculate the value of the test statistic. Locate the calculated test statistic on your figure in part (a) and state your conclusion
Questions & Answers
QUESTION:
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. (a) Define the test statistic and a critical region that has an = 0.05 significance level. Sketch a standard normal pdf illustrating this critical region. (b) If y1 = 37 and y2 = 53 defectives were observed for the day and night shifts, respectively, calculate the value of the test statistic. Locate the calculated test statistic on your figure in part (a) and state your conclusion
ANSWER:Step 1 of 4
Given:
The statistical hypotheses are provided as,
Where 
The number of levers is 