Emission of Nitrous Oxide for “newer” (less than 5 years old) cars is normally d

Question

Emission of Nitrous Oxide for “newer” (less than 5 years old) cars is normally distributed. 56 newer cars were first driven with a standard fuel and then with Petrocoal (a gasoline with a methanol additive). The results of the nitrous oxide emissions test are summarized as follows

Type of fuel Average Nitrous Oxide Standard Deviation of Nitrous Oxide

Standard 1.025 0.2796

Petrocoal 1.135 0.3134

Test the null hypothesis Ho": & ' ) ' against the alternative hypothesis Ho*: & ' > ) ' at the 1%, 5%, and 10% levels of significance.

Explanation / Answer

Solution:

Here, we have to use the two sample t test for the population means. The null and alternative hypothesis is given as below:

H0: µ1 µ2

Ha: µ1 > µ2

Test statistic formula for this test is given as below:

Test statistic = t = (X1bar – X2bar) / sqrt[(S1^2/N1)+(S2^2/N2)]

We are given

X1bar = 1.025, X2bar = 1.135, S1 = 0.2796, S2 = 0.3134, N1 = 56, N2 = 56, df = 56+56 – 2 = 110

Now, plug all values in the above formula

Test statistic = t = (1.025 – 1.135) / sqrt[(0.2796^2/56)+(0.3134^2/56)]

Test statistic = t = -1.9599

P-value = 0.0263

For alpha = 1% or 0.01

P-value > Alpha value, so we do not reject the null hypothesis

For alpha = 5% or 0.05

P-value < Alpha value, so we reject the null hypothesis

For alpha = 10% or 0.10

P-value < Alpha value, so we reject the null hypothesis

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