MATHS (CONFIDENCE INTERVAL)
1. The American Community Survey (ACS), part of the United States Census
Bureau, conducts a yearly census similar to the one taken every ten years, but with
a smaller percentage of participants. The most recent survey estimates with 90%
confidence that the mean household income in the U.S. falls between $69,720 and
$69,922. Find the point estimate for mean U.S. household income and the error
bound for mean U.S. household income.
2. The average height of young adult males has a normal distribution with
standard deviation of 2.5 inches. You want to estimate the mean height of
students at your college or university to within one inch with 93%
confidence. How many male students must you measure?
3. A pharmaceutical company makes tranquilizers. It is assumed that the
distribution for the length of time they last is approximately normal.
Researchers in a hospital used the drug on a random sample of nine patients.
The effective period of the tranquilizer for each patient (in hours) was as
follows: 2.7; 2.8; 3.0; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4. Construct a 95%
confidence interval for the population mean length of time. Calculate for the
margin of error.
4. Suppose that 14 children, who were learning to ride two-wheel
bikes, were surveyed to determine how long they had to use
training wheels. It was revealed that they used them an average
of six months with a sample standard deviation of three months.
Assume that the underlying population distribution is normal.
Construct a 99% confidence interval for the mean of time using
training wheels. Calculate the error bound margin.
5. Unoccupied seats on flights cause airlines to lose revenue. Suppose a large
airline wants to estimate its mean number of unoccupied seats per flight over
the past year. To accomplish this, the records of 225 flights are randomly
selected and the number of unoccupied seats is noted for each of the sampled
flights. The sample mean is 11.6 seats and the sample standard deviation is
