Advanced Hypothesis Testing Paper

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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).


Rejection of the null hypothesis leads to the acceptance of the alternative hypothesis. The alternative hypothesis states that there is a difference between the procedures. It is denoted by H1.
Assuming that the upstream BOD and downstream BOD are normally distributed, we test using significance level of 0.05 whether BOD increases at the downstream. The significance level of a statistical hypothesis test is a fixed probability of rejecting the null hypothesis H0, when it is in fact true. It is called a type I error and is set by the investigator in relation to the consequences of such an error. We want to make the significance level as small as possible in order to protect the null hypothesis and to prevent, as far as possible, the investigator from inadvertently making false claims.
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. ...
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