Download Worksheet #7

WORKSHEET #7
STA 291
Summer 2010
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)
for n≥30
𝑥̅ ± 𝑍𝛼/2
Sample Size
𝑠
√𝑛
Sample size needed to construct a 100(1-α)% confidence interval for μ or p with a margin of error of ME.
2
𝑍
𝛼/2
2
𝑛=𝑠 (
Examples
𝑀𝐸
)
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.
Suppose a sample with 50 observations yielded a mean of 30 and a variance of 100. What would be a
95% confidence interval for the true population mean?
From a sample of 68 hot dogs it is found that Joey Chestnut can eat a hot dog and bun in 8.82 seconds.
The standard deviation is 4.2 seconds. Determine with 99% confidence the average amount of time it
takes him to each a hot dog and bun.