7-2 Estimating a Population Proportion In this section we present methods for using a sample proportion to estimate the value of a population proportion. Definition A point estimate is a single value (or point) used to approximate a population parameter.
Example The Pew Research Center conducted a survey of 1007 adults and found that 85% of them know what Twitter is. Definition A confidence interval (or interval estimate) is a range (or an interval) of values used to estimate the true value of a population parameter. A confidence level is the probability 1 – ? (often expressed as the equivalent percentage value) that the confidence interval actually does contain the population parameter, assuming that the estimation process is repeated a large number of times. Confidence intervals can be used informally to compare different data sets, but the overlapping of confidence intervals should not be used for making formal and final conclusions about equality of proportions. Critical Values A standard z score can be used to distinguish between sample statistics that are likely to occur and those that are unlikely to occur.
Definition A critical value is the number on the borderline separating sample statistics that are likely to occur from those that are unlikely to occur. Definition When data from a simple random sample are used to estimate a population proportion p, the margin of error, denoted by E, is the maximum likely difference (with probability 1 – ?, such as 0.95) between the observed proportion and the true value of the population proportion p. Round-Off Rule for Confidence Interval Estimates of p Round the confidence interval limits for p to three significant digits. Caution Never follow the common misconception that poll results are unreliable if the sample size is a small percentage of the population size.

Sample Size Suppose we want to collect sample data in order to estimate some population proportion. Round-Off Rule for Determining Sample Size If the computed sample size n is not a whole number, round the value of n up to the next larger whole number.
Example Many companies are interested in knowing the percentage of adults who buy clothing online. Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization.
Now, let us get ten independent samples (without replacement within each sample) of the original population (10% each). To estimate the number of red balls in the original population, one can calculate the average of the above list and divide by the sample. Instead of a number, how can I obtain the probability mass function of the estimated population? For Question 1, you should use a Bayesian approach with a beta prior for the proportion of red balls. Not the answer you're looking for?Browse other questions tagged confidence-interval estimation sampling inference or ask your own question. Is there an adjective for "untruthful, especially when pretending to know more than one actually does"?
Why is the laser dish in the southern hemisphere of the Death Star rather than the northern one?

For now, we do not yet use a formal method of hypothesis testing, so we simply generate a confidence interval and make an informal judgment based on the result. Using the value of the calculated margin of error E and the value of the sample proportion,, find the values of and. How many adults must be surveyed in order to be 95% confident that the sample percentage is in error by no more than three percentage points?
For question 2, as you update your prior you will see the variance shrink as you continue to sample and you can stop based on whatever criteria you are comfortable with.
Within each sample the balls are being taken without replacement, so in fact I might just be making 10 independent samples of the same population.
You can for example stop when there is a value which has a probability > 95% (this might take a while).
We can use a sample proportion to construct a confidence interval to estimate the true value of a population proportion, and we should know how to interpret such confidence intervals. The conditions for the binomial distribution are satisfied: there is a fixed number of trials, the trials are independent, there are two categories of outcomes, and the probabilities remain constant for each trial. In the Chapter Problem we noted that a Pew Research Center poll of 1007 randomly selected adults showed that 85% of respondents know what Twitter is.

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