Question

State whether the following statements true or false, and Why? 1. The type I error and type II error are related. A decrease in the probability of one generally results in an increase in the probability of the other. 2. The size of the critical region, and therefore the probability of committing a type I error, can always be reduced by adjusting the critical value(s). 3. An increase in the sample size n will reduce α and β simultaneously. 4. If the null hypothesis is false, β is a maximum when the true value of a parameter approaches the hypothesized value. The greater the distance between the true value and the hypothesized value, the smaller β will be. 5. The power of a test is the probability of rejecting H0 given that a specific alternative is true.

Answer 1

(Since there are more than 4 parts i will answer first 4)

Reality True False Correct True Type 1 error False Positive Measured or Perceived False Correct Type 2 error False Negative

TYPE 1 ERROR = α and TYPE 2 ERROR = β

1.

TRUE

as we can see from table they are clearly related ,

and if there is a decrease in one's probability the other one's probability will increase

2.

TRUE

if we reduce the critical values the critical region reduce and then the probability of error will also reduce

3.

FALSE

critical value is inversely proportional to square root of n

therefore if we increase n, critical value will decrease which will then decrease α but increase β

4.

FALSE

β or type 2 error occurs when null hypothesis is true in reality

therefore , If the null hypothesis is false, β is not required as type 2 error will not occur in this situation

P.S. (please upvote if you find the answer satisfactory)