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Answer:
(A) The mean for the differences is 2.0.
(B) The test statistic is 1.617.
(C) At 90% confidence the null hypothesis should not be rejected.
Step-by-step explanation:
We are given that a random sample of eight cars from each manufacturer is selected, and eight drivers are selected to drive each automobile for a specified distance.
The following data (in miles per gallon) show the results of the test;
Driver Manufacturer A Manufacturer B
1 32 28
2 27 22
3 26 27
4 26 24
5 25 24
6 29 25
7 31 28
8 25 27
Let = mean MPG for the fuel efficiency of Manufacturer A brand
= mean MPG for the fuel efficiency of Manufacturer B brand
SO, Null Hypothesis, :
or
{means that there is a not any significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles}
Alternate Hypothesis, :
or
{means that there is a significant difference in the mean MPG (miles per gallon) for the fuel efficiency of these two brands of automobiles}
The test statistics that will be used here is <u>Two-sample t test statistics</u> as we don't know about the population standard deviations;
T.S. = ~
where, = sample mean MPG for manufacturer A =
= 27.625
= sample mean MPG for manufacturer B =
= 25.625
= sample standard deviation for manufacturer A =
= 2.72
= sample standard deviation manufacturer B =
= 2.20
= sample of cars selected from manufacturer A = 8
= sample of cars selected from manufacturer B = 8
Also, =
= 2.474
(A) The mean for the differences is = 27.625 - 25.625 = 2
(B) <u><em>The test statistics</em></u> = ~
= 1.617
(C) Now at 10% significance level, the t table gives critical values between -1.761 and 1.761 at 14 degree of freedom for two-tailed test. Since our test statistics lies within the range of critical values of t, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which <u>we fail to reject our null hypothesis</u>.
Therefore, we conclude that there is a not any significant difference in the mean MPG (miles per gallon) when testing for the fuel efficiency of these two brands of automobiles.