Answer:
27.5+/-1.24 mi/gallon.
= ( 26.26, 28.74) mi/gallon.
Therefore, the 95% confidence interval (a,b)= ( 26.26, 28.74) mi/gallon.
Step-by-step explanation:
Confidence interval can be defined as a range of values so defined that there is a specified probability that the value of a parameter lies within it.
The confidence interval of a statistical data can be written as.
x+/-zr/√n
Given that;
Mean x = 27.5 mi/gallon.
Standard deviation r = 4 mi/gallon
Number of samples n = 49
Confidence interval = 97%
z-value (at 95% confidence) = 2.17
Substituting the values we have;
27.5+/-2.17(4.0/√49)
27.5+/-2.17(0.571428571428)
27.5+/-1.24 mi/gallon.
= ( 26.26, 28.74) mi/gallon.
Therefore, the 95% confidence interval (a,b)= ( 26.26, 28.74) mi/gallon.
