# A salesman paid 12 visits to his area sales manager and noted that he had to wait for 10,15,20,17,11,25,30,27,36,40,5 and 26 minutes, respectively, before being called in his office. The area sales manager claims that the salesmen wishing to meet him do not have to wait for more than 20 minutes before being called in. Using the sign test, verify at 0.05 level of significance the claim made by the area sales manager.

1
by smhaque0

2014-09-09T16:59:53+05:30

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Values of W = (Wait time - 20 minutes) are :

W = -10, -5, 0, -3, -9, 5, 10, 7, 16, 20, -15, 6

Mean of W = μ = 22/12 = 1.833
standard deviation = σ = 10.27

Z = normalized variable at W = 0 or wait time is 20 min
= (W-20)/σ = -1.833/10.27 = -0.1785

ZTable(-0.1785<Z<0) = ZTable(0<Z<0.1785) = 0.071 approximately

20 minutes is an average waiting time with a significance level of 7.1%.

It is not in 0.05% significance level. It is in 0.07% significance level.

The area sales manager's claim is wrong.