Question

Is there a significant difference in Highway MPG between cars weighing greater than 1.5 tons and cars weighing less than 1.5 tons? Using inferential statistics, determine whether we accept or reject the null hypothesis by showing: hypothesis, critical value, formulas, test statistics, decision/conclusions. Here is the dataset:

HighwayMPG (for cars less than 1.5 tons)	Highway MPG (for cars greater than 1.5tons)
25	20
34	20
31	21
46	21
36	22
33	22
29	23
50	23
30	23
43	23
37	24
32	24
25	24
33	24
37	25
26	25
41	25
30	25
33	25
31	26
31	26
34	26
36	26
29	26
33	26
30	26
28	26
31	26
26	27
31	27
38	27
37	28
30	28
33	28
29	28
34	28
33	28
27	28
30	28
27	28
29	29
36	29
33	30
27	30
31	30
	30
	31

Answer 1

Data Summary

	n	Mean (M)	Variance (SS)	Standard Deviation (SD)
HighwayMPG (for cars less than 1.5 tons)	45	32.5556	27.4798	5.2421
Highway MPG (for cars greater than 1.5tons)	47	25.8511	7.7382	2.7818

The null and alternative hypotheses are   
Ho : μ1 = μ2                             μ1, μ2 are the population means for the two types of cars respectively
Ha : μ1 ≠ μ2   
   
Let α = 0.05                    Level of Significance
We use independent Samples T test since population standard deviation is unknown   
Using the formulae given below, we get   
We use following formulae for computation

df1 = n1 - 1 df2 = n2 - 1 df = n1 + n2 - 2

Degrees of Freedom    
df1 = 44                df2 = 46   
df = 90    
    
Pooled Variance Sp²    
Sp² = 17.3897    
    
Mean Squared Error S_(M1-M2)    
S_(M1-M2) = 0.8697    
    
t-statistic    
t-statistic = 7.7087   
For t = 7.7087   df = 90   we find the Two Tailed p-value using Excel function t.dist.2t    
p-value = t.dist.2t( 7.7087, 90)    
p-value = 0    
    
Decision    
0 < 0.05    
that is p-value < α    
Hence we REJECT Ho    
    
Conclusion    
There exists enough statistical evidence at α = 0.05 to show that     
there is a significant difference in Highway MPG between cars weighing greater than 1.5 tons     
and cars weighing less than 1.5 tons