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In: Math

17. You run a hypothesis test to see whether the average price of gas is higher...

17. You run a hypothesis test to see whether the average price of gas is higher than the reported value of $2.53. You find a p-value of .001 and reject Ho. a. Which type of error could you be committing here, Type 1 or Type 2? 18. In a jury trial, the jury makes a decision, and they could be right or wrong. Describe how a type 1 error could happen in this situation, and how a type 2 error could happen in this situation. Which error do you believe is worse to commit and why? (This is just your own opinion.) 21. Bob’s local pizza place claims it delivers pizzas in 30 minutes on average. Bob is convinced it’s more than that. He does a hypothesis test and gets a p-value of .001. a. What does Bob conclude? b. If Bob made the wrong conclusion what error did he make? c. What would be the impact of his error?

Solutions

Expert Solution

(17)

Since we have rejected H0, we could have committed Type I Error: Rejection of a true null hypothesis.

(18)

H0: Null Hypothesis: The culprit is innocent

HA: Alternative Hypothesis: The culprit is not innocent.

Type I Error: Rejection of a true null hypothesis. Suppose in reality, the culprit is innocent. But, the jury wrongly concludes that the culprit is not innocent. Type I Error is committed in this situation.

Type II Error: Failure to eject of a false null hypothesis. Suppose in reality, the culprit is not innocent. But, the jury wrongly concludes that the culprit is innocent. Type II Error is committed in this situation.

Type I Error is more serious because in this situation the jury is unnecessarily punishing an innocent person.

(19)

(a)

Since p = 0.001 is less than , the difference is significant. Reject null hypothesis and conclude that Bob’s local pizza place delivers pizzas in more than 30 minutes on average.

(b)

If Bob made the wrong conclusion , it implies that he has rejected a true null hypothesis: Type I Error.

(c)

The impact of this error is that Bob will think wrongly that Bob’s local pizza place delivers pizzas in more than 30 minutes on average, whereas in reality it is not so. Unnecessarily Bob will be blaming his local pizza place.

milcah answered 7 months ago
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