M 384G/374G, Fall 04
Understanding confidence intervals
Decide which of the following best fits the statement given: Accurate statement,
ambiguous (might be correct or incorrect depending on the interpretation),
needs more detail to be accurate, definitely wrong, just gives the intuitive
idea, reasonable conclusion, nonsense.
1. If we calculate the 95% confidence interval (1.2 , 3.1) for a mean µ,
then the probability that 1.2 < µ < 3.1 is 0.95.
2. If we have calculated a 90% confidence interval 55 < µ <
58 for a mean µ, then 90% of the time, µ will be between 55 and
58.
3. In calculating a 90% confidence interval 55 < µ < 58 for
a mean µ, we use a method which, in repeated sampling with simple random
samples of the same size, will give an interval containing µ about 90%
of the time.
4. In calculating a 90% confidence interval 55 < µ < 58 for
a mean µ, we use a method which for about 90% of all possible simple
random samples of the same size will give an interval containing µ
5. If we have calculated a 90% confidence interval 55 < µ <
58 for a mean µ of a variable y, then in repeated sampling, the sample
mean will lie in the interval (55, 58) for about 90% of all samples.
6. If we have correctly calculated the 95% confidence interval (1.2 , 3.1)
for a mean µ from a simple random sample, then we can be pretty confident
that µ is greater than zero.