![]() ![]() Test, at the 10% level of significance, whether the data provide sufficient evidence to conclude that the new system will provide a tighter control of dissolved oxygen in the tanks. The samples yield the following information: New Sample 1: n 1 = 31 s 1 2 = 0.0121 Old Sample 2: n 2 = 16 s 2 2 = 0.0319 Thirty-one water samples from a tank operated with the new system were collected and 16 water samples from a tank operated with the old system were collected, all during the course of a day. A new system is evaluated against the old one currently being used in terms of the variance in measured dissolved oxygen. The fish hatchery looks to upgrade their water monitoring systems for tighter control of dissolved oxygen. Dissolved oxygen in tank water is very tightly monitored by an electronic system and rigorously maintained at a target level of 6.5 milligrams per liter (mg/l). In a particular fish hatchery newly hatched baby Japanese sturgeon are kept in tanks for several weeks before being transferred to larger ponds. Japanese sturgeon is a subspecies of the sturgeon family indigenous to Japan and the Northwest Pacific. The three forms of the alternative hypothesis, with the terminology for each case, are: The null hypothesis always has the form H 0 : σ 1 2 = σ 2 2. This is not a problem, since σ 1 = σ 2 precisely when σ 1 2 = σ 2 2, σ 1 σ 2 precisely when σ 1 2 > σ 2 2. ![]() A smaller standard deviation among items produced in the manufacturing process is desirable since it indicates consistency in product quality.įor theoretical reasons it is easier to compare the squares of the population standard deviations, the population variances σ 1 2 and σ 2 2. For example, if the random variable measures the size of a machined part in a manufacturing process, the size of standard deviation is one indicator of product quality. Standard deviation measures the variability of a random variable. In some practical situations the difference between the population standard deviations σ 1 and σ 2 is also of interest. Click the Calculate button to calculate the Students t-critical value. A test based on an F statistic to check whether two population variances are equal.In Chapter 9 "Two-Sample Problems" we saw how to test hypotheses about the difference between two population means μ 1 and μ 2. one tailed t test critical value calculator - This quick calculator allows you to calculate a critical valus for the z, t, chi-square, f and r distributions. ![]()
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