Calculate standard error population proportion

Commonly Used Multipliers Multiplier Number (z*) Where z* is a multiplier number that comes form the normal curve and determines the level of confidence (see Table 9.1 for some common multiplier numbers). The Normal Approximation tells us that the distribution of these random errors over all possible samples follows the normal curve with a standard deviation of Sample proportion = population proportion + random error. In Lesson 8Р’В we learned what probability has to say about how close a sample proportion will be to the true population proportion. We know that estimates arising from surveys like that are random quantities that vary from sample-to-sample. (0.7731, 0.8269) We estimate with 90% confidence that the true percent of all students in the district who are against the new legislation is between 77.31% and 82.69%.A random sample is gathered to estimate the percentage of American adults who believe that parents should be required to vaccinate their children for diseases like measles, mumps, and rubella.Compute a 97% confidence interval for the true percent of students who own an iPod and a smartphone. In a sample of 300 students, 68% said they own an iPod and a smart phone.Compute a 90% confidence interval for the true percent of students who are against the new legislation, and interpret the confidence interval.She surveys 600 students and finds that 480 are against the new legislation. The confidence interval is (0.564, 0.636).Р”Р„ student polls his school to see if students in the school district are for or against the new legislation regarding school uniforms.

Ninety percent of all confidence intervals constructed in this way contain the true value for the population percent of students that are registered voters.

Alternate Wording: We estimate with 90% confidence that between 56.4% and 63.6% of ALL students are registered voters.

We estimate with 90% confidence that the true percent of all students that are registered voters is between 56.4% and 63.6%.

The confidence interval for the true binomial population proportion is (pРІР‚Р† РІР‚вЂњ EBP, pРІР‚Р† + EBP) = (0.564,0.636). The random variable PРІР‚Р†(read РІР‚СљP primeРІР‚Сњ) is that proportion, To form a proportion, take X, the random variable for the number of successes and divide it by n, the number of trials (or the sample size). (There is no mention of a mean or average.) If X is a binomial random variable, then X ~ B( n, p) where nР’В is the number of trials and p is the probability of a success. How do you know you are dealing with a proportion problem? First, the underlying distribution is a binomial distribution. The procedure to find the confidence interval, the sample size, the error bound, and the confidence level for a proportion is similar to that for the population mean, but the formulas are different. Confidence intervals can be calculated for the true proportion of stocks that go up or down each week and for the true proportion of households in the United States that own personal computers. Businesses that sell personal computers are interested in the proportion of households in the United States that own personal computers.

Investors in the stock market are interested in the true proportion of stocks that go up and down each week. Often, election polls are calculated with 95% confidence, so, the pollsters would be 95% confident that the true proportion of voters who favored the candidate would be between 0.37 and 0.43: (0.40 РІР‚вЂњ 0.03,0.40 + 0.03). For example, a poll for a particular candidate running for president might show that the candidate has 40% of the vote within three percentage points (if the sample is large enough). Calculate the sample size required to estimate a population mean and a population proportion given a desired confidence level and margin of errorР”Вuring an election year, we see articles in the newspaper that state confidence intervals in terms of proportions or percentages.

Calculate standard error population proportion