A small lawnmower company produced 1,500 lawnmowers in 2005. In
an effort to determine how maintenance-free these units were, the
company decided to conduct a multiyear study of the 2005
lawnmowers. A sample of 200 owners of these lawnmowers was drawn
randomly from company records and contacted. The owners were given
an 800 number and asked to call the company when the first major
repair was required for the lawnmowers. Owners who no longer used
the lawnmower to cut their grass were disqualified. After many
years, 186 of the owners had reported. The other 14 disqualified
themselves. The average number of years until the first major
repair was 6.3 for the 186 owners reporting. It is believed that
the population standard deviation was 1.28 years. If the company
wants to advertise an average number of years of repair-free lawn
mowing for this lawnmower, what is the point estimate? Construct a
95% confidence interval for the average number of years until the
first major repair.