Question

Below are the hydrocarbon emissions at idling speed, (in parts per million, ppm) of a random sample of eighteen 1990 model cars.

39 135 40 152 41 153 62 162 70 185 81 260 103 302 110 328 132 332

Use the WSRT to determine if there is sufficient evidence to indicate that the median hydrocarbon emission at idling speed is under 180 ppm. (alpha = .05).

Answer 1

Ho:median=180

H1: median <180

treatment 1	treatment2	sign	abs difference	Rank	sign rank
39	180	-1	141	16	-16
135	180	-1	45	5	-5
40	180	-1	140	15	-15
152	180	-1	28	4	-4
41	180	-1	139	14	-14
153	180	-1	27	3	-3
62	180	-1	118	12	-12
162	180	-1	18	2	-2
70	180	-1	110	11	-11
185	180	1	5	1	1
81	180	-1	99	10	-10
260	180	1	80	9	9
103	180	-1	77	8	-8
302	180	1	122	13	13
110	180	-1	70	7	-7
328	180	1	148	17	17
132	180	-1	48	6	-6
332	180	1	152	18	18

The sum of positive ranks is:=58

and the sum of negative ranks is:=113

test stat = min{W+,W- } = 58

The critical value for the signficance level α=0.05 provided, and n= 18 , the type of tail specified is T*=47, and the null hypothesis is rejected if T≤47.

since, T>47,do not reject Ho

hence,   there is not sufficient evidence to indicate that the median hydrocarbon emission at idling speed is under 180 ppm.