For a new car model from Company M, engineers proposed a slight tweak in the engine design that could lead to better fuel efficiency. To test this, 10 cars were randomly assigned the originally designed motor, and their average miles per gallon was 27.90. Another 10 cars were randomly assigned the motor with the tweaked design, and their average miles per gallon was 25.62. Miles per gallon are normally distributed for both motor designs and assume a variance of 0.97 miles per gallon for both engines. If μ₁ = mean miles per gallon of cars with the original motor, and μ₂ = mean miles per gallon of cars with the tweaked motor, at 5% significance,
a) Write the null and alternative hypothesis.
b) Calculate the value of the Z statistic.
c) Determine what the p-value is.
d) Is H₀ rejected?
e) Write a statistical conclusion.