In a study of an Oil field, 100 permeability measurements have been usedand resulted in a normal distribution for the permeability with a mean of 68 µD and a standard deviation of 10 µD. If we accept 10% error in the mean calculation, determine the confidence coefficient that will be adopted.
Level of significance:
The level of significance or α is the probability of rejecting H0 when, in fact, H0 is true. Rejecting H0 when it is true is an error or mistake. So, the level of significance is the probability of making a mistake, specifically termed as the probability of Type I error.
Researchers, naturally, want to minimize the probability of this mistake. Here, it was fixed at some convenient value (10%), so that this error probability cannot exceed 0.1 amount.
Even when H0 is true, there is a small chance that the test results are really extreme.
A level of significance of 0.1 means that, for an extreme value, we will wrongly reject H0 in not more than 10% cases. In other words, you set a test result value (critical value) beforehand, such that, the probability of getting a test result more extreme than the critical value would be only 0.1 or 10%, which is quite low. If in your test, you do get a value more extreme than the critical value you have set, then you reject H0 while keeping in mind that there is a 5% chance that you are making the wrong decision.
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