Question

Will Medal Need help!
What is the formula for the confidence interval? Then, define what each variable represents.

Answer 1

@ParthKohli @Hero @amistre64 @ganeshie8

Answer 2

The confidence interval for a \((1-\alpha)\%\) confidence level is given by
\[\large \bigg(\theta_0-Z_{\alpha/2}\frac{\sigma}{\sqrt n},~\theta_0+Z_{\alpha/2}\frac{\sigma}{\sqrt n}\bigg)\]
\(\theta_0\) is the measured statistic, \(Z_{\alpha/2}\) is the cuttoff/critical value, and \(\dfrac{\sigma}{\sqrt n}\) is the standard error. \(\sigma\) is the population standard deviation (if known) or can be estimated by a sample standard deviation. \(n\) is the sample size.

The cutoff value depends on the test you wish to use, and \(\theta_0\) depends on the statistic you wish to estimate.

Answer 3

Can you help with another question?

Answer 4

sure

Answer 5

What conditions must be met before constructing a confidence interval for a proportion? Be sure to be specific with regard to whether you use p or p-hat in your check.

Answer 6

Had to look it up, wasn't entirely sure myself: http://stattrek.com/estimation/confidence-interval-proportion.aspx

Answer 7

Not quite sure what it is saying. Can you summarize it for me?

Answer 8

Sampling must be random: this is to avoid bias withing the sample so that the true population proportion is accurately estimated.

At least 10 successes/failures: I think this means that the sample must contain a somewhat balanced ratio of successes to failures. So if we have ten trials for test, for instance, we want a sampling that is more along the lines of 4 successes/6 failures as opposed to 1 success/9 failures.

Answer 9

Do you have time for one more question?

Answer 10

The state agriculture department asked random samples of Indiana farmers in each county whether they favored a mandatory corn checkoff program to pay for corn product marketing and research. In Tippecanoe County, 263 farmers were in favor of the program and 252 were not. In neighboring Benton County, 260 were in favor and 377 were not.

a. Find the proportions of farmers in favor of the program in each of the two counties.

b. Compute a 95% confidence interval for the difference between the proportions of farmers favoring the program in Tippecanoe County and in Benton County. Do you think opinions differed in the two counties?

Answer 11

@SithsAndGiggles