Review the chapter readings of this week and reflect the following concepts:
- What is the sampling distribution of the population variance and what are the properties of this distribution?
- What is the alternative of the z statistic for normally distributed populations which eliminates some limitations of the central limit theorem and what are the properties of this distribution?
- Sampling distribution of the population variance is obtained by population variance divided by the sample size. The sample size implies the number of scores applicable in calculating the mean (Zikmund et al., 2013). The smaller the sample size, the larger the variance of the mean of the sampling distribution. The sampling distribution of the population variance is based on three statistical groupings that determine the appropriate statistical technique applicable. The groups are univariate, bivariate, and multivariate statistical analyses. Univariate statistical analyses tests involve one variable, bivariate involves two variables and multivariate analysis tests involve more than two variables (Zikmund et al., 2013).
The alternative of Z statistics is t statistics. In t-statistics, a univariate t-test is conducted for testing a hypothesis containing a particularly observed mean against a specific value. Like the standardized normal curve, t-distribution is a distribution with a standard deviation of 1.0 and a mean of 0 represented symmetrically in a bell-like shape. For a larger sample size, say 30 and above, the values obtained from z-distribution and t-distribution are similar. The t-distribution is characterized by the following critical aspects; first, the distribution applies to comparisons involving ratio measures or the mean of an interval. Secondly, the population size must not exceed 30 for the values to be distinct and different from those of Z-statistics. Thirdly, the symmetrical bell-shaped distribution in t-statistics is determined by degrees of freedom (df). The degree of freedom is obtained by subtracting assumptions or the number of constraints needed to compute a statistical term from the total number of observations. Unlike bivariate and multivariate t-tests, the degrees of freedom (df) in univariate analysis tests are equal to the sample size minus one (Zikmund et al., 2013).
Zikmund, W. G., Babin, B. J., Carr, J. C., & Griffin, M. (2013). Business Research Methods. (9th ed.). Cengage Learning.