Question

How do you decide whether to reject or fail to reject the null hypothesis?

How do you tell whether the test is left, right, or two tailed?

Why can we never accept the null hypothesis?

Why does decreasing the probability of making a type one error increase the probability of making a type two error?

How does a researcher decide the level of significance for a hypothesis test?

Answer 1

• In testing of hypothesis, after observing the data, we make inference about our population. In testing of hypothesis, we set our null and alternative hypothesis. Then, we construct a test statistic. The distribution of test-statistic is known when null hypothesis is true. Then, from the observed sample, we calculate the value of our test-statistic. Then, based on our level of significance, we find the critical region. We reject our null hypothesis if the value of test-statistic falls in the critical region. Otherwise, we fail to reject null hypothesis.
• A test whether it is left, right r two-tailed is completely dependent on the nature of the alternative hypothesis. It will be very clear when by the following example. Suppose, we test a conjecture about the mean() of a population of interest. Let's say historically, . Then we might be interested in knowing whether against the null hypothesis that , then, if the
• The test of hypothesis is designed such a way that, if there is significant evidence to claim the rejection of null hypothesis, then we say null is rejected. But, if there is no evidence, i.e the sample does not fall in the rejection region, that means there is no strong evidence in favor of alternative, but that does not mean null is true, it might or might not be true.
• As discussed earlier, the decision of accepting or rejecting the null hypothesis is dependent on the criticial region or rejection region. Let be the entire sample space and R be the rection region. i.e if the sample falls inside R we will reject null otherwise we will fail to reject null. Now, type I error means probability of rejecting null when it is true. Now, if we shrink the rejection region R then, the probability that we reject null will decrease and automatically we will decrease the probability of type-I error. But, on the other hand, shrinking R means we will enlarging the accepting region i.e. , which means we increase the probability of not rejecting null, which in turn increases the probability of type-II error.
• The level of significane is the probability of type-I error, i.e probability of false rejection of null hypothesis. Based on situation, depending on how much risk the researcher can take of falsely rejecting null, and depending on its impact, they decides the level of significance as 5%, 10% or 1%.