Question

The costs, in dollars, per load of laundry were measured for independent random samples of 18 loads using high-efficiency detergents (like those used in many front-loading washing machines) and 17 loads using standard detergents. The results are shown in the following table:

Standard (X)						High Efficiency (Y)
0.23	0.13	0.28	0.30	0.25	0.18	0.18	0.19	0.15	0.06	0.18	0.18
0.14	0.13	0.29	0.18	0.12	0.20	0.15	0.09	0.05	0.13	0.13	0.15
0.56	0.18	0.14	0.13	0.20		0.09	0.08	0.30	0.18	0.08	0.12

The data is provided again below, now pooled and ordered. Record the rank of each observation in the space above the corresponding value. Report your answers as either integers (no decimal) or half-integers (ending in .5) as appropriate.

0.05	0.06	0.08	0.08	0.09	0.09	0.12	0.12

0.13	0.13	0.13	0.13	0.13	0.14	0.14	0.15	0.15	0.15

0.18	0.18	0.18	0.18	0.18	0.18	0.18	0.19	0.20	0.20

0.23	0.25	0.28	0.29	0.30	0.30	0.56

Answer 1

The ranks of each observation are below.

The rank of any observation is number of observations less than or equal to the value of observation. We have given same rank for equal values.

1	2	3	3	5	5	7	7
0.05	0.06	0.08	0.08	0.09	0.09	0.12	0.12

9	9	9	9	9	14	14	16	16	16
0.13	0.13	0.13	0.13	0.13	0.14	0.14	0.15	0.15	0.15

19	19	19	19	19	19	19	26	27	27
0.18	0.18	0.18	0.18	0.18	0.18	0.18	0.19	0.20	0.20

29	30	31	32	33	33	35
0.23	0.25	0.28	0.29	0.30	0.30	0.56