CK-12 Probability and Statistics - Advanced

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%

2. 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

2. 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.


3. 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