Question

Researchers wanted to know if the females are pickier in their ratings of the quality of the restrooms than males; or, if the quality of the facilities rating is independent of gender. A survey was

conducted of 100 randomly selected travelers who used a certain gas station restroom. Here are the results.

Quality of Restroom Facility

	Above Average	Average	Below Average	Total
Female	8	24	31	63
Male	9	34	8	51
Total	17	58	39	114

a. What percent of the respondents were female?

b. What percent of the respondents said the restrooms were above average?

c. What percent of the respondents were females who said the restroom was below average?

d. What percent of males said the restrooms were average?

e. What percent of respondents who rated the restrooms below average were male?

f. Find the marginal distribution (percentages) for sex.

g. Find the marginal distribution (percentages) for quality of restroom facility.

h. Find the conditional distribution (percentages) for quality of restroom facility for females.

Answer 1

(a)

Out of 114 respondents, 63 were female so

P(female) = 63 /114 = 0.5526

Answer: 55.26%

(b)

Out of 114 respondents, 17 are above average so

P(above average) = 17 /114 = 0.1491

Answer: 14.91%

(c)

Out of 39 respondents who said restroom were below average, 31 were female so

P(female | below average) = 31 /39 = 0.7949

Answer: 79.49%

(d)

P(average | males) = 34 / 51 = 0.6667

Answer: 66.67%

(e)

P(male | below average) = 8 / 39 = 0.2051

Answer: 20.51%

(f)

The marginal distribution for sex are:

P(male) = 51 /114 = 0.4474 =44.74%

P(female) = 63 /114 = 0.5526 = 55.26%

(g)

P(above average) = 17 /114 = 0.1491 = 14.91%

P(average) = 58 /114 = 0.5088 = 50.88%

P(below average) = 39 /114 = 0.3421 = 34.21%

(h)

P(above average|female) = 8 / 63 = 0.1270 = 12.70%

P(average|female) = 24 /63 = 0.3810 = 38.10%

P(below average\female) = 31 /63 = 0.4921 = 49.21%