Download The gas mileage for a certain model of car is known to have a

8.1B Confidence Interval Example
The gas mileage for a certain model of car is known to have a standard deviation of 5 mi/gal. A
simple random sample of 64 cars of this model is chosen and found to have a mean gas mileage
of 27.5 mi/gal. Construct a 95% confidence interval for the mean gas mileage for this car model.
“Inference Toolbox”
Steps for constructing a confidence interval:
Step 1:
Identify the population of interest and the parameter you want to draw
conclusions about.
We are interested in estimating the mean gas mileage μ for this car model.
Step 2:
Choose (State) the appropriate inference procedure.
Verify the conditions for using the selected procedure.
STATE: We will construct a one-sample z confidence interval.
CONDITIONS:

RANDOM: The problem states that the 64 cars compose a SRS.

NORMAL: The sample size is large (64).

INDEPENDENT: 10% Rule – 64*10 = 6400. It is reasonable to believe that
there is at least 6400 cars manufactured for a specific model.
All the conditions are met.
Step 3:
If the conditions are met, carry out the inference procedure.
CI = Estimate +/- Margin of Error
CI = x-bar ± z* σ/ √n
27.5 ± 1.96 ∙ 5 / √64
27.5 ± 1.225
(26.275, 28.725)
Step 4:
Interpret your results in the context of the problem.
We are 95% confident that the interval from 26.275 to 28.725 mi/gal captures the
true mean gas mileage for a certain model of car.
The volume of bottles of soda from an assembly line is known to have a standard deviation of
0.076 liters. A quality control inspector tested the volume of 36 randomly selected bottles of
soda from the assembly line and obtained a mean volume of 1.98 liters. Find the 98%
confidence interval for the mean volume of all bottles from the assembly line.