Questions about the Mean, Confidence Intervals and the Central Limit Theorem.
(written at Notre Dame to cover material in Chapter 6 of SAS System for Elementary Statistical Analysis)
Click on the answer you think is most nearly correct.
1. Confidence intervals for the mean are appropriate for:
Nominal data. Ordinal or ratio data. Interval or nominal data. Interval or ratio data. Ordered data.
2. Which of the following statement is not true:
Even if the sample values are not normally distributed, the sample average is approximately normally distributed. Stratified random sampling can often allow you to take a smaller sample overall. The standard deviation of the distribution of sample averages is called the standard error of the mean. The bound of the difference between the sample average and the population mean is called the bound on the error of estimation. The larger the sample size the more difficult it is to estimate the population mean.
3. The following statement is not true: In accordance with the Central Limit Theorem,
you are drawing a simple random sample from a population with a mean, u, and a standard deviation, sigma. "n" must be reasonably large. the sample average is approximately normally distributed with mean, u, and variance, sigma-squared. as the sample size "n" approaches infinity the sample average converges in distribution to a normal distribution. the underlying simple random variable must be normally distributed.
4. Which of the following statement is not true:
One of the practical implications of the Central Limit Theorem is that you can use the Empirical Rule to summarize the distribution of sample averages. The Central Limit Theorem essentially says that sample averages from all types of distributions are nearly normally distributed for large enough samples. Since the normal distribution represents variables that can range in value from minus infinity to plus infinity, then for all practical purposes we cannot use the normal distribution for variables that can only take on positive values. TINV is a built-in function is SAS that gives you the t-value that corresponds to a specified confidence level with specified degrees of freedom. The sample average is a point estimate of the population mean.
5. The following statement is not true: In repeated samples the sample average will tend to be closer to the true population mean when:
the population variance is large. the standard error of the sample average is small. more observations are sampled. the population mean is large relative to the population standard deviation. The sample size is big.