Can someone please do a step by step solution for this problem! Thank you! :D Em

Question

Can someone please do a step by step solution for this problem! Thank you! :D

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: Test the null hypothesis H_0: Sigma_X^2 lessthanorequalto Sigma_Y^2 of against the alternative hypothesis H_1: Sigma_X^2 > Sigma_Y^2 at the 1%, 5%, and 10% levels of significance.

Explanation / Answer

Solution:

Here, we have to use the F test for checking the given null and alternative hypothesis.

Null hypothesis: H0: x2 y2

Alternative hypothesis: Ha: x2 > y2

We are given

x2 = 0.3134*0.3134 = 0.09822

y2 = 0.2796*0.2796 = 0.078176

n1 = 56, n2 = 56, df1 = 55, df2 = 55

Test statistic = F = S12 / S22 = 0.09822 / 0.078176 = 1.2564

P-value = 0.2000

For level of significance or alpha value = 1% or 0.01

Upper critical value = 1.8878

P-value > Alpha value

Test statistic < Upper critical value

So, we do not reject the null hypothesis

For level of significance or alpha value = 5% or 0.05

Upper critical value = 1.5643

P-value > Alpha value

Test statistic < Upper critical value

So, we do not reject the null hypothesis

For level of significance or alpha value = 10% or 0.10

Upper critical value = 1.4163

P-value > Alpha value

Test statistic < Upper critical value

So, we do not reject the null hypothesis

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