Question

In a study of nitrogen dioxide (NO₂) pollution within vehicles, three models of cars were driven for 1 hr in a town area (A) and an adjacent country area (B). Triethanolamine disc was installed in each car to record the mean nitrogen dioxide concentration over the 1 hr period.

Vehicle model	Nitrogen dioxide (ppb)
	Area A	Area B
1	17.4	12.3
1	11.8	18.2
1	12.5	19.0
2	32.3	21.8
2	38.1	41.0
2	34.2	38.6
3	21.6	16.4
3	36.0	19.8
3	23.0	15.7

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Given that the distribution of data is normal and the variances are equal, what will be the appropriate test to determine the effect of vehicle model and location of the drive on NO₂ concentration within the vehicle?

Select one:

a. Scheirer-Ray-Hare Test

b. Two-way ANOVA

c. Two independent sample t test

d. One-way ANOVA

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What will be the null hypothesis?

(1)  NO₂ concentration is equal among different vehicle models.

(2)  NO₂ concentration is unequal among different vehicle models.

(3)  No interaction between vehicle models and locations of drive on the NO₂ concentration.

(4)  There is interaction between vehicle models and locations of drive on the NO₂ concentration.

(5)  NO₂ concentration is equal between different driving locations.

(6)  NO₂ concentration is unequal between different driving locations.

Select one:

a. (2), (4) and (6)

b. (2) and (6)

c. (1), (3) and (5)

d. (1) and (5)

e. None of the above

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What is the calculated test statistics for the interaction effect?

Select one:

a. 0.93

b. 1.68

c. 16.20

d. 3.88

e. 0.13

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What are the appropriate conclusions?

Select one:

a. NO₂ concentration is equal between different locations (calculated statistics > 4.75, p-value > 0.5).

b. There is a significant interaction between vehicle models and locations of drive on the NO₂ concentration (calculated statistics > 3.89, p-value > 0.05).

c. NO₂ concentration is unequal among different vehicle models (calculated statistics > 3.89, 0.01 < p-value < 0.05).

d. NO₂ concentration is unequal between different locations (calculated statistics > 4.75, p-value < 0.05).

e. There is no significant interaction between vehicle models and locations of drive on the NO₂ concentration (calculated statistics < 3.89, p-value > 0.05).

Answer 1

using excel>data>data analysis>two way anova

we have

Anova: Two-Factor With Replication
SUMMARY	Area A	Area B	Total
1
Count	3	3	6
Sum	41.7	49.5	91.2
Average	13.9	16.5	15.2
Variance	9.31	13.39	11.108
2
Count	3	3	6
Sum	104.6	101.4	206
Average	34.86667	33.8	34.33333
Variance	8.743333	109.44	47.61467
3
Count	3	3	6
Sum	80.6	51.9	132.5
Average	26.86667	17.3	22.08333
Variance	63.05333	4.81	54.60167
Total
Count	9	9
Sum	226.9	202.8
Average	25.21111	22.53333
Variance	104.2436	103.4325
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Sample	1127.054	2	563.5272	16.19745	0.00039	3.885294
Columns	32.26722	1	32.26722	0.927456	0.354531	4.747225
Interaction	116.8611	2	58.43056	1.679468	0.227468	3.885294
Within	417.4933	12	34.79111
Total	1693.676	17

Ans 1 )we will use

b. Two-way ANOVA

Ans2 )

What will be the null hypothesis?

(1)  NO2 concentration is equal among different vehicle models.

(3)  No interaction between vehicle models and locations of drive on the NO2 concentration.

(5)  NO2 concentration is equal between different driving locations.

c. (1), (3) and (5)

Ans 3) the calculated test statistics for the interaction effect

b. 1.68

Ans 4 )conclusion

e. There is no significant interaction between vehicle models and locations of drive on the NO2 concentration (calculated statistics < 3.89, p-value > 0.05).