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WORKSHEET #8
STA 291 (022-024)
3/19/08
Confidence Intervals
A confidence interval gives an estimated range of values which is likely to include an unknown
population parameter, the estimated range being calculated from a given set of sample data.
A confidence interval is based on three elements:
(a) a value of a point estimator (the sample mean, etc.)
(b) the standard error of the point estimator; and
(c) the critical value of Z or t (e.g., the 95% confidence interval or the 99% confidence interval).
Confidence Intervals for a single Mean (μ)
normal population with σ known
σ unknown and n ≥ 30
σ unknown and n < 30
Sample Size
Sample size needed to construct a 100(1-α)% confidence interval for μ with a margin of error of B.
Examples
A survey of 100 retailers revealed that the mean after-tax profit was $90,000 with a standard deviation
of $15,000. Determine the 95% confidence interval of the mean after-tax profit for all retailers.
During a water shortage, a water company randomly sampled residential water meters in order to
monitor daily water consumption. On a particular day, a sample of 100 meters showed a sample mean
of 250 gallons. It is already known that the standard deviation of daily water consumption is 50 gallons.
Provide a 90% confidence interval of the mean water consumption for the population.
The number of rooms rented daily during the month of February (28 days) has a mean of 37 rooms per
day and a standard deviation of 23 rooms per day. Use this information to estimate the number of
rooms rented daily during February with 95% confidence.
A statistician wants to estimate the mean weekly family expenditure on clothes. He believes that the
standard deviation of the weekly expenditure is $125. Determine with 95% confidence the number of
families that must be sampled to estimate the mean weekly family expenditure on clothes to within $15.