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

Answer:

A

Step-by-step 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;