What is the difference between confidence level and confidence interval?

statistics help, sampling, interval, hypotheisis 4 multiple choice

• 1. The level of significance in hypothesis testing is the probability of a. not rejecting a true null hypothesis b. no rejecting a false null hypothesis c. rejecting a true null hypothesis d. could be any of the above, depending on the situation e. none of the above answers is correct 2. In determining the same size [n] necessary to estimate a population proportion[p], which of the following information is NOT needed? a. the maximum size of the sampling error that can be tolerated b. the confidence level required c. a preliminary estimate of the true population proportion[p] d. the mean of the population[u] e. none of the above answers is correct 3. if we consider the simple random sampling process as an experiment, the sample mean[x] is a. always zero b. always smaller than the population mean[u] c. a random variable d. exactly equal to the population mean[u] e. none of the above answers is correct 4. A 95% confidence interval for a population mean[u] show the values 25.1 to 28.3. What is the appropriate conclusion? a. 95% of all sample means[x] should be between 25.1 and 28.3 b. 95% of the time the population mean[u] will be within this interval: 5% of the time it will be outside of this interval c. Since 95% of all confidence intervals contain the population mean [u], we are 95% confident this interval include it d. All of the above answers is correct e. None of the above answers is correct

• Answer:

  Hello icahn! Here are the answers to your questions. 1. C The level of significance is the probability of committing a Type I error; while a Type I error is defined as rejecting the null hypothesis when it's actually true. Please check the following page for more information. Hypothesis Testing http://smccd.net/accounts/case/biol690/hypothesis.html 2. D In the link that follows you can find the formula needed to calculate the required sample sample size. Calculating this number implies that you want to set a maximum sampling error (a) (as more people will reduce this error); set a desired confidence level (b); and you also need to have an estimate for the variance of the population. Since we're talking about proportions, the variance is calculated as n*p*(1-p), therefore, an estimate for p needs to be known. We don't need the mean of the population, the sample proportion will naturally tend to be "near" this number. Determining a sample size involves setting a desires dispersion around the mean, but the mean is not needed to calculate this dispersion. How To Determine Sample Size http://www.isixsigma.com/library/content/c000709.asp 3. C In the following link (page 3) you can find why the sample mean is a random variable. It's the sum of independent and identically distributed random variables (each observation), divided by the sample size, so it's itself a random variable. http://giant.lakeheadu.ca/~wzhuang/4030/4030-lec8.pdf 4. E None of the statements is correct. The correct answer would be that we are 95% confident that the population mean is within this interval (that's the definition of a confidence interval); however, this is not due to the fact that "95% of all confidence intervals contain the population mean", so answer C is not correct. Google search strategy "determine sample size" "sample mean" "random variable" "level of significance" I hope this answers your question. If you have any doubt regarding my answer, please request a clarification. Otherwise I await your rating and final comments. Best regards! elmarto