Hypothesis Test of the Difference Between Two PAIRED Means.

Im pretty sure this should be a one tailed test, as does my teacher does an example for this and her's had one tail. Help me understand which tail it is (what lead you to believe it was right or left tail.) I will need the test statistic and critical value(s). You will need the null and alternative (H0: u1=u2, H1: u1=/=u2).

The equation that is needed to solve this is t= d *bar* - U_d / (Sd/*square root* of n)

D.O.F formula to be used is n-1.

This is all the infomartion I think you need might need to determine the kind of problem this is.

I've asked this question before but it seems I didn't provide enough information and the answers included two tailed test or something else.

Oh also I need these formulas to be used, as in no excel to speed things up because as much as i like shortcuts I need to understand this concept.

Standard dev or Sx should be 1.414213562. Pretty sure this is right, not 100%. d *bar* should = -2, pretty sure on that. D.O.F should be 10-1=9. alpha =0.1.

yeah so thats all i got please take your time to show as much detail as you can, im not a picky person but the test wont care so i have to sound kind of rude to ask of you so much.

May this find you at a convenient time. Much obliged!

The test statistic is
Round your answer to 2 decimal places.

Ten randomly selected cars were filled with either regular or premium gas (the decision was made based on a coin toss) and then
driven on the freeway for the entirety of the tank of gas. The next day, each car was filled with whichever type of gas that was not
used the previous day and then driven on the freeway for the entirety of the tank of gas. The mileage for each day was recorded and is
summarized in the table below.
MPG of 10 cars (regular/premium): 13/19, 20/22, 21/24, 23/25, 22/25, 27/26, 25/26, 27/28, 28/32, 22/24.
Car 1
Car 2
Car 3
Car 4
Car 5
Car 6
Car 7
Car 8
Car 9
Car 10
Regular 16
20
21
23
22
27
25
27
28
22
Premium 19
22
24
25
25
26
26
28
32
24
You will using a 90% confidence level to test the claim that there is a difference between the efficiency rates of premium and regular
gas.
You may assume that both samples are drawn from normally distributed populations.
*Please let the regular gas mpg be sample 1 and the premium gas mpg be sample 2.*

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