You give the latest test for “Belief in Santa Claus” from Canadian Living magazi

Question

You give the latest test for “Belief in Santa Claus” from Canadian Living magazine to your little brother. According to the test, if the child answers more than 10 of the questions with the correct “Santa answer”, then the child is declared to still believe in Santa Claus. From that perspective, describe with reference to the test (a) what would be a Type I error for the test? (b) what would constitute a Type II error for the test? (c) what would correspond to the power of the test? (d) what corresponds to the criterion of the test?

Explanation / Answer

Here we are trying to test whether the child believes in santa claus, according to the criterion for the test given here, the null and the alternate hypothesis given here are:

H0: Child do not believe in santa claus

H1: Child do believe in santa claus

a) The type I error for the test is the event when the null hypothesis is rejected given that it is true. Here it means when we incorrectly conclude that the child believes in santa claus even though in reality he does not

b) The type I error for the test is the event when the null hypothesis is retained given that it is false. Here it means when we incorrectly conclude that the child do not believe in santa claus even though in reality he does.

c) The power of the test is the probability of rejecting the null hypothesis when it is false. Here it means the probability of concluding that the child belives in santa claus when in reality he does believe in santa claus

d) The decision criteria here is given in the problem as: if the child answers more than 10 of the questions with the correct “Santa answer”, then the child is declared to still believe in Santa Claus

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