![calculate standard error of proportion calculate standard error of proportion](https://i.ytimg.com/vi/3ReWri_jh3M/maxresdefault.jpg)
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.
![calculate standard error of proportion calculate standard error of proportion](https://i2.wp.com/variationtheory.com/wp-content/uploads/2018/06/Slide1-2.png)
The confidence interval is (0.564, 0.636).Ī 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.
![calculate standard error of proportion calculate standard error of proportion](https://i.ytimg.com/vi/qcBMckOgB0w/maxresdefault.jpg)
![calculate standard error of proportion calculate standard error of proportion](https://i.ytimg.com/vi/siqx4PbqJ6s/maxresdefault.jpg)
The random variable P′(read “P prime”) 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 n 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 – 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).