Question

The data found below measure the amounts of greenhouse gas emissions from 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 vehicle 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
7.6 6.2 6.4
6.1 7.6 7.5
6.1 6.7 7.4
6.7 7.5 6.6
7.4 7.7 6.1
7.4 7.5 7.5
5.9 5.8 6.6
5.9 6.8 6.3
6.2 7.3
7.4
What are the hypotheses for this​ test?
A. H0​: μ1 = μ2 = μ3
H1​: μ1 ≠ 2μ ≠ μ3
B. H0​: μ1 = μ2 = μ3
H1​: At least one of the means is different from the others.
C. H0​: μ1 ≠ μ2 ≠ μ3
H1​: μ1 = μ2 = μ3
D. H0​: At least one of the means is different from the others.
H1​: μ1 = μ2 = u3
Determine the test statistic.
F = ________
What is the critical F​ value?
F = _________
Identify the​ P-value.
​P-value = __________
What is the conclusion of the​ test?
_________ the null hypothesis. Conclude that the type of vehicle ______________ appear to affect the amount of greenhouse gas emissions for these three types.

Answer 1

Answer:

1.

A. H0 :  μ1 = μ2 = μ3

Ha : μ1 ≠ 2μ ≠ μ3

2. Test Statistics = 95%

3. Critical F-Value = 3.76

4. P-Value = 2.32

5. Conclusion : Reject the null hypothesis

6. Type of vehicle does effect the amount of green house gas emissions.

Step-by-step explanation:

The correct order of the steps of a hypothesis test is given following  

1. Determine the null and alternative hypothesis.

2. Select a sample and compute the critical value F-test for the sample mean.

3. Determine the probability at which you will conclude that the sample outcome is very unlikely.

4. Make a decision about the unknown population.

These steps are performed in the given sequence to test a hypothesis.

The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 95% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value.

Answer 2

A. H 0  μ1 = μ2 = μ3

Ha  μ1 ≠ 2μ ≠ μ3

2. Test Statistics is 95%

3. Critical F-Value is 3.76.

4. P-Value is 2.32.

5. Conclusion  Reject the null hypothesis.

6. Type of vehicle does effect the amount of green house gas emissions.

The correct order of the steps of a hypothesis test is given below.

1. Determine the null and alternative hypothesis.

2. Select a sample and compute the critical value F-test for the sample mean.

3. Determine the probability at which you will conclude that the sample outcome is very unlikely.

4. Make a decision about the unknown population.

All steps are performed in the given sequence to test a hypothesis.

The null hypothesis is rejected or accepted on the basis of level of significance. When the p-value is greater than level of significance we fail to reject the null hypothesis and null hypothesis is then accepted. It is not necessary that all null hypothesis will be rejected at 95% level of significance. To determine the criteria for accepting or rejecting a null hypothesis we should also consider p-value.

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