Question

In the interest of detecting the few children remaining who believe in Santa Claus, you give...

In the interest of detecting the few children remaining who believe in Santa Claus, 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 or more of the questions with the correct “Santa answer”, then the child is declared to believe
in Santa Claus. From that perspective, describe with reference to the test

(a) what would be a Type I error for the test? (1 point)
(b) what would constitute a Type II error for the test? (1 point)
(c) what would correspond to the power of the test? (1 point)
(d) what corresponds to the criterion of the test? (2 points)

Math   Statistics-And-Probability   
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Answer #1

a)

Type 1 error. Rejecting bull hypothesis when it is true. Null hypothesis is child does not believe in Santa claus

When it was true that child does not believe in Santa claus but we conclude that child believes in Santa Claus, it constitute type 1 error.

b)

Type 2 error - when null hypothesis is accepted as true when actually it was false.

When we fail to conclude that child believes in Santa claus when in reality the child does believe in Santa claus

c)

Power of test correspond to probability of correctly rejecting null hypothesis when it was false.

When we conclude that child believes in Santa claus when in reality the child does believe in Santa claus

d)

Criterion of test is based on the probability of getting statistic measured in sample if value stated in null hypothesis is true

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