The practice final which has been made available to you has several problems relating to material on sample means, confidence intervals, and hypothesis testing. In particular, you should be able to do the following:

• Given a population mean, a sample size, and a population or sample standard deviation, know the probability that a sample mean will fall within a certain range (e.g., between 2 and 10).
• Given a sample size and either a sample mean and standard deviation or a sample proportion, report a X% confidence interval for the population mean or population proportion.  Also be able to report the standard deviation of the sample mean or proportion.  Know how to do this for the means of small samples as well as large samples.
• Given a sample mean, sample size, and a sample standard deviation, test the hypothesis that the population mean is a certain number.
• Given a sample proportion and sample size, test the hypothesis that the population proportion is a certain number.
• Given a pair of independent samples, with their respective sample mean, sample standard deviation, and sample sizes, test the hypothesis that the samples come from populations with the same mean.
• Given a pair of independent samples, with their respective sizes and sample proportions, test they hypothesis that the samples come from a population with the same proportion.
• Given a paired set of samples, test the hypothesis that the pairs have the same mean across the two samples.
• Compute the covariance and the correlation coefficient given a sample.  You should also know how to perform a significance test on the correlation coefficient.
• Compute the regression coefficient given the covariance, sample size, and variances of the two variables.  You should also know how to compute the standard error of the regression coefficient and test a hypothesis that it equals zero.
  

In addition, you should be familiar with the following ideas:

• Consider a variable that takes on the value "true" with probability p and the value "false" with probability 1-p.  If we have a sample of n independent observations of such a random variable from a finite population if size N, of whom K take on the value "true" in the population, the distribution of "trues" in the sample is hypergeometrically distributed with parameters n, N and K.
• The central limit theorem: (1) Requires that the variable of interest have a finite mean and variance; (2) requires that observations in the sample of interest be independent and identically distributed; (3) requires that the sample size be over 30; (4) allows us to conclude that if the first three criteria are satisfied, then the sample mean will be normally distributed regardless of the underlying distribution of the variable.
• The sample mean is more accurate the larger the sample, and less accurate the larger the variance of the underlying distribution.
• Hypothesis tests are performed in the following order: (1) A null hypothesis and alternative hypothesis are stated; (2) a level of significance is decided on; (3) A test statistic is decided on; (4) A decision rule is decided on; (5) The sample is collected, the statistic is computed, and the decision is made.
• A Type I error occurs when a true null hypothesis is rejected.  The probablility of a type I error, known as alpha, is equal to the significance level of the test.  A Type II error occurs when a false null hypothesis is not rejected.  The probability of a Type II error is known as beta and is given by the probability value of the sample mean under the alternative hypothesis.