Question

The data found below measures the amounts of greenhouse gas emissions from randomly three types of vehicles. The measurements are in tons per year, expressed as CO2 equivalents. Use a 0.05 significance level to test the claim that the different types of vehicles have the same mean amount of greenhouse gas emissions. Based on the results, does the type of vehicle appear to affect the amount of greenhouse gas emissions?

Type A	Type B	Type C
5.6	8.7	9.6
6.9	7.7	9.8
5.6	8.1	9.6
5.8	8.3	9.4
6.3	7.7	8.8
5.8	7.4	9.4
5.5	8.5	9.1
7.2	7.1	9.5
6.1		8.5
7.4

a) State the null and alternative hypothesis (2 points).

b) Check the requirements (3 points)

c) Carry out the hypothesis test (make sure you write everything down) (3 points).

d) What is your conclusion? (2 points)

Answer 1

a)

Hypotheses are:

H0:  The different types of vehicles have the same mean amount of greenhouse gas emissions.

Ha:  The different types of vehicles do not have the same mean amount of greenhouse gas emissions.

In symbols:

b)

Following is the output of descriptive statistics:

Since largest standard deviation 0.705 is less than 2 times of smallest devitaion 0.421 so equal variance assumptions has been fulfilled. Each type is independent from other.  

c)

Following table shows the groups totals:

	Type A, G1	Type B, G2	Type C, G3
	5.6	8.7	9.6
	6.9	7.7	9.8
	5.6	8.1	9.6
	5.8	8.3	9.4
	6.3	7.7	8.8
	5.8	7.4	9.4
	5.5	8.5	9.1
	7.2	7.1	9.5
	6.1		8.5
	7.4
Total	62.2	63.5	83.7

Following table shows the grand total and sum of squares of values:

	G	G^2
	5.6	31.36
	6.9	47.61
	5.6	31.36
	5.8	33.64
	6.3	39.69
	5.8	33.64
	5.5	30.25
	7.2	51.84
	6.1	37.21
	7.4	54.76
	8.7	75.69
	7.7	59.29
	8.1	65.61
	8.3	68.89
	7.7	59.29
	7.4	54.76
	8.5	72.25
	7.1	50.41
	9.6	92.16
	9.8	96.04
	9.6	92.16
	9.4	88.36
	8.8	77.44
	9.4	88.36
	9.1	82.81
	9.5	90.25
	8.5	72.25
Total	209.4	1677.38

d)

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