A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random sample of seven cars were selected and were driven for two weeks without the booster and two weeks with the booster. Use the definitions of X1 and X2 as given in the table. Consequently, D = X1 – X2. Test the effectiveness of the octane booster at α=0.05. Assume that the normality assumption is satisfied. Gasoline Mileage
Without booster, X1
(mpg)
Gasoline Mileage without booster, X1 (mpg) Gasoline Mileage With booster, X2(mpg)
21.2 23.8
25.4 25.6
20.9 22.4
27.6 28.3
22.8 24.5
27.3 28.8
23.4 25.2
1. What critical value should be used at a = 0.05?
2. Determine the mean of the differences.
3. State the alternative hypothesis?
4. Compute the standard deviation of the differences.

i can you with this question sweetie!

step-by-step explanation:

the answer is:

the correct option:

b.

to solve the problem, we need to remember how to operate to simplify exponential expressions using the logarithms.

we are given the equation:

then, using placing logarith with base 7 on both sides of the equation, we have:

so, rounding the obtained result to two decimal places (nearest hundreth), we have:

hence, we have that the correct option:

b.

have a nice day!

image for option 4

step-by-step explanation:

i just know the internet

the image is given below

since the options are not given so we draw it from the equation

the given equation is

y = (x-1) (x+4)

y = y² + 3x - 4

the above equation is a quadratic equation which will have two roots. if we draw the graph for it, it will look like this