A sample of 51 elements is selected to estimate a 95% confidence interval for the variance of the population. The chi-square values to be used for this interval estimation are -1.96, 32.357, 71.420, 34.764, 67.505, 12.8786, and 46.9630.
We are interested in testing whether the variance of a population is significantly less than 1.44. The null hypothesis for this test is H0: Ļ^2 = 1.44.
A sample of 41 observations yielded a sample standard deviation of 5. If we want to test H0: Ļ = 20, the test statistic is 51.25.
The value of F with numerator and 19 denominator degrees of freedom is 2.48, 2.58, 3.63, or 2.96.
To avoid the problem of not having access to tables of the F distribution with values given for the lower tail, the numerator of the test statistic should be the one with the larger sample size.