Some manufacturers claim that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones. Suppose that consumers test 279 hybrid sedans and get a mean of 27 mpg with a standard...

Some manufacturers claim that non-hybrid sedan cars have a lower mean miles-per-gallon (mpg) than hybrid ones. Suppose that consumers test  279  hybrid sedans and get a mean of  27  mpg with a standard deviation of  5.25  mpg. Also,  250  non-hybrid sedans get a mean of  26  mpg with a standard deviation of  6.25  mpg. Suppose that both populations are known to be normal distributed.

Conduct a hypothesis test to evaluate the manufacturers' claim. Test at a  2%  level of significance.

Let  population  1  denote non-hybrids and population  2  denote hybrids.

(a)  H0 :  μ1     μ2

(b)  Ha :  μ1     μ2

(c) In words, state what your random variable represents.

The random variable is the (mean/difference in mean/difference in the) miles per gallon of non-hybrid sedans and hybrid sedans.

(D) What is the test statistic?


Round your answer to three decimal places

(E) What is the p-value?


Round your answer to three decimal places.
p-value =

(F)

1. Alpha:


2. Decision:  (reject/decline to reject)


3. Reason for decision: p-value   ( >  or <_ ) =""  ="">


4. Conclusion: There  (is/ is not) sufficient evidence to conclude that the mean miles per gallon of non-hybrid sedans is less than that of hybrid sedans.