Question

List the four possible results of the combinations of decisions and true states of nature for a test of hypothesis. Which of the following lists the four possible results of the combinations of decisions and true states of nature for a test of​ hypothesis? A. Reject Upper H 0H0 when Upper H 0H0 is​ true; insufficient evidence to reject Upper H 0H0 when Upper H 0H0 is​ true; reject Upper H 0H0 when Upper H Subscript aHa is​ true; insufficient evidence to reject Upper H 0H0 when Upper H Subscript aHa is true B. Reject Upper H 0H0 when Upper H 0H0 is​ true; insufficient evidence to reject Upper H 0H0 when Upper H Subscript aHa is​ true; reject Upper H Subscript aHa when Upper H Subscript aHa is​ true; insufficient evidence to reject Upper H 0H0 when Upper H 0H0 is true C. Reject Upper H 0H0 when Upper H Subscript aHa is​ true; insufficient evidence to reject Upper H 0H0 when Upper H 0H0 is​ true; reject Upper H Subscript aHa when Upper H 0H0 is​ true; insufficient evidence to reject Upper H 0H0 when Upper H Subscript aHa is true D. Reject Upper H 0H0 when Upper H 0H0 is​ true; insufficient evidence to reject Upper H 0H0 when Upper H 0H0 is​ true; reject Upper H 0H0 when Upper H Subscript aHa is​ true; accept Upper H Subscript aHa when Upper H 0H0 is true

Answer 1

A

Explanation:

The combinations of decisions and true states of nature for a test of​ hypothesis is given below:

• When
  `H_o` is True, Accept
  `H_o`

• When
  `H_o` is True, Reject
  `H_o` (Type I Error)
• When
  `H_o` is False, Accept
  `H_o` (Type II Error)
• When
  `H_o` is False, Reject
  `H_o`

Note that when
`H_o` is False, then the Alternate Hypothesis,
`H_a` is True.

Therefore Option A gives the possible combinations.

The possible choices in Option A are ordered below to correspond to the results above.

• Insufficient evidence to reject
  `H_o` when
  `H_o` is​ true;
• Reject
  `H_o` when
  `H_o` is​ true; Type 1 Error
• Insufficient evidence to reject
  `H_o` when
  `H_a` is true -Type II Error
• Reject
  `H_o` when
  `H_a` is​ true;