B1.2
MARGIN OF ERROR FOR A POPULATION MEAN IS KNOWN
The question:
The gas mileage for a certain model of car is known to have a standard deviation of 5 m/g. A simple random sample of 64 cars of this model is chosen and found to have a mean gas mileage of 27.5 m/g. Construct a 95% confidence interval for the mean gas mileage for this car model. Interpret the interval in words.
The question stem: What are they asking you to determine?Construct a 95% confidence interval for the mean gas mileage for this car model. Interpret the interval in words.
What are you given?
The gas mileage for a certain model of car is known to have a standard deviation of 5 m/g. A simple random sample of 64 cars of this model is chosen and found to have a mean gas mileage of 27.5 m/g. Construct a 95% confidence interval for the mean gas mileage for this car model. Interpret the interval in words.
*simple random sample
* = 27.5 m/g
*n = 64 cars of this model
* = 5 m/g
*95% confidence in the results, which means critical value is 1.96
The formula: for a One Sample Z Interval (ZInterval)
Identify your variables:
Question type: Z-interval, Note: You will use the Interval functions in the calculator when you are preparing a confidence interval.
Calculation: Using the T1-83: Z Interval
Select STAT -> TEST -> Z Interval. Note select stats not data in this case
You will need , calculate This gives you a confidence interval of (26.275, 28.725)
Interpretation:
We are 95% confident that the mean gas mileage for this model of car falls between 26.275 and 28.725.
