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An aquaculture farm takes water from a stream and returns it after it has circulated through the fish tanks. The owner thinks that, since the water circulates rather quickly through the tanks, there is little organic matter in the effluent. To find out if this is true, he takes some samples of the water at the intake and other samples downstream the outlet and tests for Biochemical Oxygen Demand (BOD)…
It is a hypothesis which states that there is no difference between the procedures and is denoted by H0. The following test of hypothesis can be conducted from the table above:
Test Statistic: It is the random variable X whose value is tested to arrive at a decision. The Central Limit Theorem states that for large sample sizes (n > 30) drawn randomly from a population, the distribution of the means of those samples will approximate normality, even when the data in the parent population are not distributed normally. A z statistic is usually used for large sample sizes (n > 30), but often large samples are not easy to obtain, in which case the t-distribution can be used. The population standard deviation s is estimated by the sample standard deviation, s.
Rejection Region: It is the part of the sample space (critical region) where the null hypothesis H0 is rejected. The size of this region is determined by the probability (a) of the sample point falling in the critical region when H0 is true. a is also known as the level of significance, the probability of the value of the random variable falling in the critical region. Also it should be noted that the term "Statistical significance" refers only to the rejection of a null hypothesis at some level a. ...
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