Question

Given the following scenario:

a) State H_o and H_a

b) State Type I and Type II Error

c) Give the ramifications of each type of error

d) Describe which (in your opinion) is worse and why.

answer the above (a-d ) chart is optional

1. I am going scuba diving over spring break. I am trying to decide if I should spend the money and have my regulator (what you breathe through under water) checked out for possible defects and serviced before the trip.

2. A recent blood test showed an abnormality. Do I spend the money and time to have further tests done or wait and see if the test next year has the same abnormality?

3. The “idiot you are almost out of gas” gauge on my car is on. I am driving to the state basketball playoffs in Nampa. Do I stop and fill up the gas tank and arrive late or try and make it without filling up. The light has been on for a couple of days now.

Answer 1

(1)

(a)

H0: Null Hypothesis: There is no defect in regulator

HA: Alternative Hypothesis: There is defect in regulator

(b)
Type I Error: Rejection of a true null hypothesis.

Type II Error: Failure to reject a false null hypothesis.

Suppose in reality there is no defect in regulator. But we concude there is defect in regulator. Type I Error is committed in this situation.

Suppose in reality there is defect in regulator. But we concude there is no defect in regulator. Type II Error is committed in this situation.

(c)

The consequence of Type I Error is that we will be unnecessarily checking our regulator and wasting our time and money which is not at all required since in reality there is no defect in regulator.

The consequence of Type II Error is that we will not be checking our regulator which is very much required since in reality there is defect in regulator.

(d)

Type II Error is more serious because if we do not repair the regulator we will have problem in actual usage of the same.

(2)

(a)

H0: Null Hypothesis: There is no problem in my blood pressure.

HA: Alternative Hypothesis: There is problem in my blood pressure.

(b)
Type I Error: Rejection of a true null hypothesis.

Type II Error: Failure to reject a false null hypothesis.

Suppose in reality there is no problem in my blood pressure. But we concude there is problem in my blood pressure. . Type I Error is committed in this situation.

Suppose in reality there is problem in my blood pressure.. But we concude there is no problem in my blood pressure. Type II Error is committed inthis situation.

(c)

The consequence of Type I Error is that we will be unnecessarily checking our blood pressure and wasting our time and money which is not at all required since in reality there is no problem in my blood pressure..

The consequence of Type II Error is that we will not be checking our blood pressure which is very much required since in reality there is problem in my blood pressure.

(d)

Type II Error is more serious because if we do not attend to my blood pressure, my health will detoriate which is not at all desirable.

(3)

(a)

H0: Null Hypothesis: There is enough gas in my car.

HA: Alternative Hypothesis: There is not enough gas in my car.

(b)
Type I Error: Rejection of a true null hypothesis.

Type II Error: Failure to reject a false null hypothesis.

Suppose in reality . there is enough gas in my car. But we concude there is not enough gas in my car.. Type I Error is committed in this situation.

Suppose in reality there is not enough gas in my car. But we concude there is enough gas in my car.. Type II Error is committed in this situation.

(c)

The consequence of Type I Error is that we will be unnecessarily filling gas in car and wasting our time which is not at all required since in reality there is enough gas in my car..

The consequence of Type II Error is that we will not be filling gas in car which is very much required since in reality there is not enough gas in my car..

(d)

Type II Error is more serious because if we do not fill gas in car we will have problem on the way.