SOLUTION: Two new subcompact cars are tested to see if they get the same mileage. Fifteen Synglets were tested and they averaged 42.75 mpg with s = 1.57 mpg. Eight Gustos were also tested, a

Algebra ->  Probability-and-statistics -> SOLUTION: Two new subcompact cars are tested to see if they get the same mileage. Fifteen Synglets were tested and they averaged 42.75 mpg with s = 1.57 mpg. Eight Gustos were also tested, a      Log On


   

Question 1161975: Two new subcompact cars are tested to see if they get the same mileage. Fifteen Synglets were tested and they averaged 42.75 mpg with s = 1.57 mpg. Eight Gustos were also tested, averaging 40.33 mpg with s = 3.54 mpg. Assume that the samples were taken from normally distributed populations. Test the hypothesis at the 0.05 level of significance that these cars get the same mileage.
a. State the hypotheses and identify the claim.
b. Find the critical value(s).
c. Compute the test value.
d. Make the decision.
e. Summarize the results.
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
Ho: S=C mpg
Ha: they are not equal
alpha is 0.05 p{reject Ho|Ho true}
test is a t but df is more complicated, Could use 15+8-2=21. This is an issue, because others will say to use the smaller sample size in which case the df would be 7.
reject if |t|> critical value
With a calculator, the complicated df can be dealt with
t=(s-c)/ sp*(1/sqrt(n1)+1/sqrt(n2))
STAT TESTS 4 ENTER
with df=21 the critical value is 2.086
t=1.83 which is not greater than the critical value. Fail to reject based on these data.
p-value is 0.10.
Here, the variances are not likely to be equal, which makes the df calculation more difficult. The calculator gave a more conservative estimate of about 8.5. With equal variances, the df would be 21.