Confidence Interval of a Proportion

A point estimator is:

• the actual value of a parameter of a distribution.

• a statistic that provides an estimate of a population parameter.

• any statistic of a sample.

• the best estimate of a population parameter based on prior knowledge.

An experimenter is interested in the proportion of Hershey's kisses that land flat when tossed in the air. She tosses 50 and 16 land flat. A point estimate is

• p = 0.32

• p-hat = 0.32

• p = 16

• p-hat = 16

Based on a random survey, a 95% confidence interval for the proportion of voters that support Candidate A is (0.16, 0.26). The best interpretation of this confidence interval is:

• We are 95% confident that the interval from 0.16 to 0.26 captures the true proportion of voters that support Candidate A.

• The proportion of voters that support Candidate A is likely between 0.16 and 0.26.

• The proportion of voters that support Candidate A is between 0.16 and 0.26.

• The probability that the true proportion of voters who support Candidate A is in the interval (0.16, 0.26) is 0.95.

The margin of error of an estimate describes

• the maximum distance the true population value varies from the estimate.

• how far, at most, we expect the estimate to vary from the true population value.

• the number of standard deviations we expect the estimate to vary from the true population value.

• the standard deviation of the sampling distribution.

To calculate the upper bound of a confidence interval of a proportion, use

• (point estimate)

• (point estimate) + (confidence level)(std dev)

• (critical value)(point estimate)

• (point estimate) + (critical value)(std dev)

To calculate a 95% confidence interval, the critical value is:

• 1.64

• 1.96

• 2.33

• 1.28

To calculate a 96% confidence interval, the critical value is:

• 1.96

• 2.05

• 1.75

• 2.02

The three conditions you should check before constructing a confidence interval are:

• Random; Normal; Independent

• Random; Normal; Central Limit Theorem

• Normal; Large Counts; 10% rule

• Any sampling method; Large Counts; 10% Rule