Question

Consider a hypothesis test to decide whether the mean cost to community hospitals per patient per day in Ohio exceed the national mean. Answer the following questions.

a. " The mean cost to community hospitals per patient per day in Ohio does not exceed the national mean but the result of the sampling leads to the conclusion that the mean cost to community hospitals per patient per day in Ohio exceeds the national mean " is a

A. Type II error

B. correct decision

C. Type I error

b. " The mean cost to community hospitals per patient per day in Ohio exceeds the national mean but the result of the sampling does not lead to the conclusion that the mean cost to community hospitals per patient per day in Ohio exceeds the national mean " is a

A. Type I error

B. correct decision

C. Type II error

c. " The mean cost to community hospitals per patient per day in Ohio exceeds the national mean and the result of the sampling leads to the conclusion that the mean cost to community hospitals per patient per day in Ohio exceeds the national mean " is a

A. correct decision

B. Type II error

C. Type I error

d. " The mean cost to community hospitals per patient per day in Ohio does not exceed the national mean and the result of the sampling does not lead to the conclusion that the mean cost to community hospitals per patient per day in Ohio exceeds the national mean " is a

A. Type I error

B. correct decision

C. Type II error

Answer 1

Let's write the null hypothesis ( H₀ ) and the alternative hypothesis (H₁ ) from the given claim.

a) If we reject the null hypothesis which is true on the basis of sample data then Type I error is occur.

Therefore correct choice of question ( a) is C ) Type I error.

b) If we fail to reject null hypothesis which is in actual false on the basis of sample data then Type II error occur.

Therefore correct choice of question ( b) is C ) Type II error.

c) Here we reject null hypothesis and so we accept the alternative hypothesis. So we find the correct decision from the sample data.

So correct choice of ( c ) is A ) Correct Decision.

d) Here the result of the sampling does not lead to the conclusion that the mean cost to community hospitals per patient per day in Ohio exceeds the national mean. So we fail to reject the true null hypothesis. So there is no error in the decision.

SO correct choice is B) Correct decision.