7.4. Confidence Intervals http://www.ck12.org
Review Answers
1.
pˆ=
x
n
pˆ±z
√
pˆ( 1 −pˆ)
n
pˆ=
142
250
0. 568 ± 2. 56
√
0. 568 ( 1 − 0. 568 )
250
pˆ= 0. 568 0. 568 ± 0. 080
The interval is from 0. 488 to 0. 648 OR from 48 .8%to 64 .8%
- The 99% confidence interval could be narrowed by increasing the sample size from 250 to a larger number.
1.
pˆ±z
√
pˆ( 1 −pˆ)
n
pˆ±z
√
pˆ( 1 −pˆ)
n
0. 61 ± 1. 645
√
0. 61 ( 1 − 0. 61 )
300
0. 61 ± 2. 56
√
0. 61 ( 1 − 0. 61 )
300
from 0.564 to 0. 656 from 0.555 to 0. 665
pˆ±z
√
pˆ( 1 −pˆ)
n
0. 61 ± 1. 96
√
0. 61 ( 1 − 0. 61 )
300
from 0.538 to 0. 682
- The confidence interval got wider as the confidence level increased. To increase the probability of enclosing
the population proportion a wider confidence interval must be chosen. - Yes, all three confidence intervals would capture the population proportion if it were 0.58.
Vocabulary
Binomial Experiment
A type of survey or experiment in which there is a fixed number of trials that have one of only two outcomes.
The probability of success for any trial is equal to the population proportion and remains the same for every
trial. The outcomes for each trial are independent of one another and the binomial random variable,x, is the
number of successes observed inntrials.
Confidence Interval
An interval of plausible values for a population parameter. Any of the values in the interval could be used to
define a population for which the defined sample statistic would be a likely outcome.
Confidence Level
The probability that the method used to calculate the confidence interval will produce an interval that will
enclose the population parameter.
Interval Estimator
Another name for a confidence interval