Download Confidence Interval Quiz (OSM)

Confidence Interval Quiz (OSM)
NAME_____________________________
National Fuelsaver Corporation manufactures the Platinum Gasaver, a device they claim “may increase
gas mileage by 22%.” Here are the percent changes in gas mileage for 15 identical vehicles, as presented
in one of the company's advertisements:
48.3
28.7
46.9
28.7
46.8
24.8
44.6
10.8
40.2
10.4
38.5 34.6
6.9 -12.4
33.7
1. Describe the population of interest and the parameter you want to draw conclusions about.
Parameter – mean percent change in gas mileage
Population of interest – vehicles using this device (the corporation is making a claim that seems to be
about all vehicles that use this device, but note … the SAMPLE in this case is not really from the
population of interest, and this is a concern as we’ll not be able to generalize to all members of the
population.)
2. We are not told what the population standard deviation is, so we’ll have to approximate it from our
data, which means we’ll be using a t-distribution to model the sampling distribution of the mean. In
using the t model for the sampling distribution, certain assumptions must be made. Give a concise
justification that each of these assumptions is reasonably met.
Independence and Normality
SRS? We are not told this is a random sample, so we might not be able to generalize to the population.
n<10% of N? The sample of 15 vehicles is much smaller than the population.
Normality? The distribution of sample data, although not perfectly symmetric, appears to be roughly
symmetric and single-peaked, and with a sample size of 15, the t-distribution should be okay.
3. Calculate and write all the values needed to construct a 95% confidence interval for the population
mean, and report the resulting interval.
(df = n-1 = 14).
4.
Interpret this confidence interval in context. Based on this interval, do you think the company’s
claims are reasonable? Why or why not?
I am 95% confident the true mean percent change in gas mileage is between 18.9% and 38.6%.
The company’s claims are reasonable, but only for the type of vehicle used in this sample, because their
stated value of 22% is in the interval we just calculated.