
Confidence Intervals
Worksheet 1
Open the
interactive version of the normal tables. (Opens a separate browser window.)
 Because of slight irregularities that constantly
occur on a production line, cars of identical
make are not identical in every fashion. One way
in which they vary is their gas mileage. Consider
the new Toyanda RV4. The car's mechanical
operation is based on a current Toyanda model;
engineers expect the variation in gas mileage
from car to car to have a normal distribution
with standard deviation 0.35. What they don't
know is the average gas mileage for the RV4. To
find out, they take an SRS of 32 RV4s and drive
each, recording gas mileage (mpg). The sample
mean is 35.28.
 Use this data to construct a 90% CI for
the mean gas mileage of all RV4s.
 Interpret your result.
 Compute a 99% confidence interval (same
data).
 How do the margins of error for your two
intervals compare?
 An independent consumer agency can only
afford to select an SRS of 8 for testing;
the sample mean for these 8 is 35.23.
What is this agency's 90% CI for the mean
gas mileage of all RV4s?
 Compare margin of error for the two 90%
CIs you've computed.
 What is the average playing time of all Jill's
CDs? As usual, Jill is too socially involved to
take a census. Therefore, she decides to take an
SRS of 12 CDs to estimate this average. Her
friend Jack tells her that playing times of CDs
are approximately normally distributed with
standard deviation 4.27 minutes. (Jack has a lot
of free timehe's learned this by collecting data
from a CD catalog. However, his results for the
average playing time of CDs do not apply to
Jill's collection. That's because the catalog
Jack used carried all kinds of music, while Jill
is almost exclusively a fan of hardcore and
rave.) Here's the data:
55.14 46.23 53.85 43.89 42.77 44.71
44.58 47.77 48.40 50.65 46.33 50.80
 What is the
response variable?
 Identify the
population.
 Describe the
parameter that is of interest to Jill.
What is the symbol typically given to
this parameter?
 Compute the
sample mean.
 Construct a
98% CI for the mean playing time of all
Jill's CDs? What is your margin of error?
 Interpret
your CI.
 Jack's
census of the catalog finds a mean
playing time of 51.89 minutes. What can
we conclude about Jill's CD collection?

