The production manager of MPS Audio Systems Inc. is concerned about the idle tim

Question

The production manager of MPS Audio Systems Inc. is concerned about the idle time of workers. In particular, he would like to know if there is a diference in the idle minutes for workers on the day shift and the evening shift. The information below is the number of idle minutes yesterday for the five day-shift workers and the six evening-shift workers. t Evening shite 107 103 State the decision rule. Use the 001 significance level Ho: Idle minutes are the same. : lie minutes are not the same. (Negative amount should be indicated by a minus sign. Round your answers to two decimal Complete the following table (Round your answers to nearest whole numbers) 8 command option and

Explanation / Answer

Reject Ho if Z < -2.575

as for alpha = 0.01 and two sided test Z0.01,2-tailed = -2.575

Rank table

Rank sum (day) = 1 + 2 + 3 + 4 +5 = 15

Rank Sum (Night) = 6 + 7 + 8 + 9.5 + 9. 5 + 11 = 51

Test statistic = Min(15,51) = 15

Here R = n1 (n1 + n2 + 1)/ 2 = 5 * (5 + 6 + 1)/2 = 30

R = sqrt[n1 n2 (n1 + n2 + 1)/12] = sqrt [5 * 6 * 12/12] = 5.48

Z = (W - R)/ R = = (15 - 30)/ 5.48 = - 2.74

so Here Z > Zcr

so we shall reject the nul hypothesis and conclude there is significant difference in mean idle time and differrentshifts.

Day shift Rank(Day) Evening shift Rank(Night) 92 3 104 8 99 5 107 9.5 83 1 107 9.5 98 4 110 11 89 2 103 7 101 6

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