A certain chemical process is said to have produced 15 or less pounds of waste mate
every
60 lbs. batch with a corresponding standard deviation of 5 lbs. A random samp
batches gives an average of 16 lbs. of waste per batch. Test at 10 per cent level whet
average quantity of waste per batch has increased. Compute the power of the test fo
bs. If we raise the level of significance to 20 per cent, then how the power of the tes
bs. would be affected?
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Testing of hypothesis
1. Testing of Hypothesis One of the important applications of statistical inference is ‘test of hypothesis’. In testing of hypothesis, decision-making about the characteristics of the population on the basis of sample study involves the risk of taking wrong decision. For example, we may decide whether a given food-stuff is really effective in increasing weight or which of the two brands of fertilizers is more effective. In such case the modern theory of probability plays a vital role in decision-making. The branch of statistics, which helps in arriving at the criterion for such decision is called Test of Hypothesis or Hypothesis Testing or Test of Significance or Statistical Decision Making. A hypothesis is an assumption or statement, which may or may not be true about a population and is under the test. The test of hypothesis is a process of testing a significance regarding the parameter of the population on the basis of sample drawn from the population. General Procedure of Testing a Hypothesis: Formulating the Hypothesis: Hypothesis is a tentative statement of the of the population parameter on the basis of the sample study. For examples, (a) The average height of the students in a class is 160 cms. (b) A given drug cures 90% of the patients taking it. (c) A given detergent cleans better than any washing soap etc. All these hypotheses may be verified on the basis of certain sample tests. A common way of stating a hypothesis is that there is no difference between the population mean and sample mean. The term ‘no difference’ implies that the difference, if any, is merely due to sampling fluctuations. The statistical hypothesis may be divided into two types- Null hypothesis and Alternative hypothesis. Null Hypothesis: The null hypothesis is the hypothesis of no difference, which is denoted by Ho. In the above examples (a) the null hypothesis may be expressed symbolically as Ho: µ = 160 cms. While formulating a null hypothesis we should take care of the following two points. i) If we want to test the significance of the difference between statistic and the parameter or between two sample statistics then we formulate a null hypothesis that the difference is not significant. This implies that the difference is just due to fluctuations of samplin