The average mpg usage for a 2013 Toyota Prius for a sample of 10 tanks of gas wa

Question

The average mpg usage for a 2013 Toyota Prius for a sample of 10 tanks of gas was 45.5 with a standard deviation of 1.8. For a 2013 Honda Insight, the average mpg usage for a sample of 10 tanks of gas was 42.0 with a standard deviation of 2.3. Assuming different population variances, at = 0.01, is the true mean mpg lower for the Honda Insight? Sample 1: Honda Insight Sample 2: Toyota Prius Which is the right hypotheses? Write the test statistic and critical value, test result (Decision), and Conclusion.

H0: µ1 = µ2

H1: µ1 µ2

H0: µ1 µ2

H1: µ1 > µ2

H0: µ1 µ2

H1: µ1 < µ2

H0: µd 0

H1: µd < 0

H0: µ1 = µ2

H1: µ1 µ2

H0: µ1 µ2

H1: µ1 > µ2

H0: µ1 µ2

H1: µ1 < µ2

H0: µd 0

H1: µd < 0

Explanation / Answer

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   >=   0  
Ha:   u1 - u2   <   0   [HYPOTHESES]]

******************

At level of significance =    0.01          

As we can see, this is a    left   tailed test.      
Calculating the means of each group,              
              
X1 =    42          
X2 =    45.5          
              
Calculating the standard deviations of each group,              
              
s1 =    2.3          
s2 =    1.8          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    10          
n2 = sample size of group 2 =    10          
Thus, df = n1 + n2 - 2 =    18          
Also, sD =    0.923579991          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    -3.78960137   [ANSWER, TEST STATISTIC]      
              
where uD = hypothesized difference =    0          
              
Now, the critical value for t is              
              
tcrit =    -   2.55237963   [CRITICAL VALUE]  
              
Thus, as t < -2.5524,   WE REJECT THE NULL HYPOTHESIS. [DECISION]
              
Hence, there is significant evidence at 0.01 level that the true mean mpg lower for the 2013 Honda Insight. [CONCLUSION]

*****************************************************

Hi! If you use another method/formula in calculating the degrees of freedom in this t-test, please resubmit this question together with the formula/method you use in determining the degrees of freedom. That way we can continue helping you! Thanks!

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.