The chi-square distribution is skewed, but as the number of degrees of freedom becomes large, the skewness diminishes. If the number of degrees of freedom, k, is large enough, the chi-square distribution is reasonably well approximated by a normal distribution with mean k and variance 2k.

Refer to Exercise 10. Use the normal approximation to estimate the critical values and for a 95% confidence interval, and construct a 95% confidence interval for σ.

A more accurate normal approximation to is given by , where is the z-score that has area α to its right.

Exercise 10

A sample of size 101 from a normal population has sample standard deviation s = 40. The lower and upper 0.025 points of the distribution are 74.222 and . Use these values to construct a 95% confidence interval for σ.

Derrick Collins Stuart E. Bernstein Psychology 3070- 001: Research Methods Book: The Process of Research in Psychology 3 edition. Mc Bride, D.M. (2015) Notes over: Chapter 5 Variables and Measurement in Research “Dependent Variables” (99) Variables “measured or observed from an individual.” (99) “Reliability: degree to which the results of a study can be replicated...