Suppose your roommate believes the mean amount it will cost

Suppose your roommate believes the mean amount it will cost to repair your dorm refrigerator is more than $50. To determine if she is correct, suppose you perform a hypothesis test with level of significance equal to 5%. For each choice below, determine if you made the correct decision or if you made an error. If an error was made, determine if a Type-I or Type-II error was committed.

a) You conclude that the mean amount to repair a dorm refrigerator IS more than $50 when in reality the mean amount to repair a dorm refrigerator is NOT more than $50.

b) You conclude that the mean amount to repair a dorm refrigerator is NOT more than $50 when in reality the mean amount to repair a dorm refrigerator is NOT more than $50.

c) You conclude that the mean amount to repair a dorm refrigerator is NOT more than $50 when in reality the mean amount to repair a dorm refrigerator IS more than $50.

d) You conclude that the mean amount to repair a dorm refrigerator IS more than $50 when in reality the mean amount to repair a dorm refrigerator IS more than $50..

Solution

Suppose your roommate believes the mean amount it will cost to repair your dorm refrigerator is more than $50. To determine if she is correct, suppose you perform a hypothesis test with level of significance equal to 5%. For each choice below, determine if you made the correct decision or if you made an error. If an error was made, determine if a Type-I or Type-II error was committed.

a) You conclude that the mean amount to repair a dorm refrigerator IS more than $50 when in reality the mean amount to repair a dorm refrigerator is NOT more than $50.

Type I error ( rejecting true null hypothesis)

b) You conclude that the mean amount to repair a dorm refrigerator is NOT more than $50 when in reality the mean amount to repair a dorm refrigerator is NOT more than $50.

No error

c) You conclude that the mean amount to repair a dorm refrigerator is NOT more than $50 when in reality the mean amount to repair a dorm refrigerator IS more than $50.

Type II error ( fail to reject the false null hypothesis)

d) You conclude that the mean amount to repair a dorm refrigerator IS more than $50 when in reality the mean amount to repair a dorm refrigerator IS more than $50..

No error