Question

As part of an air pollution study, visibility in air was measured in three months at two altitude level.

Altitude (m)	Visibility in town air (km)
	Jan	Jun	Dec
0	13.5	3.8	14.3
0	17.2	3.3	16.9
0	18.1	7.2	21.0
0	14.3	10.5	19.7
0	19.5	9.1	18.0
50	14.5	2.8	16.5
50	17.4	3.1	16.8
50	19.1	4.2	21.6
50	20.3	6.5	19.2
50	18.5	9.1	17.0

Question 11

Given that the data neither follow normal distribution nor have equal variance, what is the appropriate test to determine if visibility varied with different months and altitude.

Select one:

a. Kruskal-Wallis Test

b. Two independent sample t test

c. Two-way ANOVA

d. Scheirer-Ray-Hare Test

Question 12

What are the degree of freedom for the altitude, month and error (Within) respectively?

Select one:

a. 1, 2, 2

b. 1, 2, 24

c. 1, 2, 4

d. 2, 3, 5

e. 2, 3, 29

Question 13

What is the conclusion for the variable altitude?

Select one:

a. Air visibility is unequal between different heights (calculated statistics = 0.015, p-value < 0.001)

b. Air visibility is equal between different heights (calculated statistics = 0.001, p-value > 0.05)

c. Air visibility is unequal between different heights (calculated statistics = 0.004, p-value < 0.05)

d. Air visibility is equal between different heights (calculated statistics = 0.015, p-value > 0.05)

Question 14

What is the conclusion for the variable Month?

Select one:

a. Air visibility is unequal among different months (calculated statistics = 9.72, 0.001 < p-value < 0.01)

b. Air visibility is unequal among different months (calculated statistics = 9.72, p-value < 0.001)

c. Air visibility is unequal among different months (calculated statistics = 25.98, p-value < 0.001)

d. Air visibility is equal among different months (calculated statistics = 25.98, p-value > 0.05)

Question 15

What is the conclusion for the interaction effect between altitude and Month?

Select one:

a. Interaction effect exists between altitude and Month (calculated statistics = 0.75, p-value < 0.05)

b. Interaction effect exists between altitude and Month (calculated statistics = 0.75, p-value < 0.01)

c. No interaction effect between altitude and Month (calculated statistics = 0.28, 0.05 < p-value < 0.1)

d. No interaction effect between altitude and Month (calculated statistics = 0.28, 0.75 < p-value < 0.90)

Answer 1

using excel>data>data analysis >two way ANOVA

we have

Anova: Two-Factor With Replication
SUMMARY	Jan	Jun	Dec	Total
0
Count	5	5	5	15
Sum	82.6	33.9	89.9	206.4
Average	16.52	6.78	17.98	13.76
Variance	6.472	10.097	6.697	33.12829
50
Count	5	5	5	15
Sum	89.8	25.7	91.1	206.6
Average	17.96	5.14	18.22	13.77333
Variance	4.838	7.013	4.712	44.67352
Total
Count	10	10	10
Sum	172.4	59.6	181
Average	17.24	5.96	18.1
Variance	5.602667	8.351556	5.086667
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
altitude	0.001333	1	0.001333	0.000201	0.98881	4.259677
Month	917.8587	2	458.9293	25.98	1.1E-10	3.402826
Interaction	12.05067	2	6.025333	0.28	0.416866	3.402826
Within	159.316	24	6.638167
Total	1089.227	29

Ans 11) here option c is true

c. Two-way ANOVA

Ans 12option b is true

b. 1, 2, 24

Ans 13 ) option b is true

b. Air visibility is equal between different heights (calculated statistics = 0.001, p-value > 0.05)

Ans  14 option c is true

c. Air visibility is unequal among different months (calculated statistics = 25.98, p-value < 0.001)

Ans 15 d is true

d. No interaction effect between altitude and Month (calculated statistics = 0.28, 0.75 < p-value < 0.90)