Question

Perform and document a two-sample hypothesis test to evaluate the claim "American cars of the past have a significantly different weight than non-americas cars of the past." Document all seven of the hypothesis testing steps.

Data from my calculations:

American Sample

MPG

X-Bar= 20.12

S= 6.36

N=247

Horsepower

X-bar= 119.74

S=39.73

N=248

Not American Sample

MPG

X-bar=29.22

S=6.67

N=151

Horsepower

X-bar=80.93

S=22.12

N=152

Data from both American and non American samples (if needed):

MPG

Mean/X-bar= 23.57

Standard Deviation= 7.84

Count= 398

Horsepower

Mean/X-bar=104.99

Standard Deviation=38.96

Count=400

Please show all work neatly (good handwriting plz), I will thumbs up for quality work :)) Neat handwriting please. No cursive

Answer 1

Objective: To test whether American cars of the past have a significantly different weight than non-americans cars of the past. The data on wights are not provided. However, probable factors (assuming, are directly proportional  related to the weight are given using which we may arrive at the objective.

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To test: American cars of the past have a significantly different MPG than non-americans cars of the past

Here, the claim to be tested as the alternative hypothesis and the negation of the claim is considered as the alternative hypothesis. Let denote the mean MPGs of American and Non- American cars of the past respectively.

To test: Vs

Given: ,   

The appropriate test to test the above hypothesis would be an Independent sample t test. Testing the assumption of homogeneity of variance assumption of this test:

To test: Vs

Test statistic:

Obtaining the p-value of the test, using excel:

We get p-value = 0.747

Since, p-value = 0.747 > 0.05, we fail to reject H0. We may conclude that the data satisfies the assumption of homogeneity of variance.Assuming that all the other assumptions of this test are satisfied, the test statistic is given by

For MPG:

Here,

Substituting the values:

  

= -2.098

Obtaining the p-value of the test, using excel:

p-value = 0.036 < 0.05

Therefore, We do have sufficient evidence to support the claim that American cars of the past have a significantly different MPG than non-americans cars of the past, based on this data at 5% level of significance.

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To test: American cars of the past have a significantly different Horsepower (HP) than non-americans cars of the past

Here, the claim to be tested as the alternative hypothesis and the negation of the claim is considered as the alternative hypothesis. Let denote the mean HPs of American and Non- American cars of the past respectively.

To test: Vs

Given: ,   

The appropriate test to test the above hypothesis would be an Independent sample t test. Testing the assumption of homogeneity of variance assumption of this test:

To test: Vs

Test statistic:

32.226

Obtaining the p-value of the test, using excel:

We get p-value = 0.000

Since, p-value = 0.000 < 0.05, we may reject H0. We may conclude that the data fails to satisfy the assumption of homogeneity of variance. However, assuming that all the other assumptions of a t test are satisfiedWe may use the t test statistic for unequal variance, given by:

= 12.536

Obtaining the p-value of the test, using excel:

p-value = 0.000 < 0.05

Therefore, We do have sufficient evidence to support the claim that American cars of the past have a significantly different HP than non-americans cars of the past, based on this data at 5% level of significance.

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Hence, since, the MPG and Horsepower of American cars are significantly different that that of the Non-American cars of the past, we may conclude that their respective weights are also significantly different.