Question

In: Math

A magazine reported that at the top 50 business schools in a​ region, students studied an...

A magazine reported that at the top 50 business schools in a​ region, students studied an average of 17.8 hours. Set up a hypothesis test to try to prove that the mean number of hours studied at your school is different from the reported 17.8 hour benchmark. Complete parts​ (a) through​ (c) below.

a. State the null and alternative hypotheses. Choose the correct answer below.

A. Upper H 0​: alpha not equals 17.8 Upper H 1​: alpha equals 17.8

B. Upper H 0​: beta not equals 17.8 Upper H 1​: beta equals 17.8

C. Upper H 0​: muequals17.8 Upper H 1​: Upper X overbarnot equals17.8

D. Upper H 0​: Upper X overbarequals17.8 Upper H 1​: Upper X overbarnot equals17.8

E. Upper H 0​: alpha equals 17.8 Upper H 1​: beta not equals 17.8

F. Upper H 0​: munot equals 17.8 Upper H 1​: Upper X overbar equals17.8

G. Upper H 0​: alphaequals17.8 Upper H 1​: alphanot equals17.8

H. Upper H 0​: muequals17.8 Upper H 1​: munot equals17.8

I. Upper H 0​: Upper X overbarnot equals17.8 Upper H 1​: Upper X overbarequals17.8

J. Upper H 0​: alphanot equals17.8 Upper H 1​: betaequals17.8

K. Upper H 0​: munot equals17.8 Upper H 1​: muequals17.8

L. Upper H 0​: betaequals17.8 Upper H 1​: betanot equals17.8

b. What is a Type I error for your​ test?

A. Concluding that the mean number of hours studied at your school is different from the reported 17.8 hour benchmark when in fact it is different

B. Concluding that the mean number of hours studied at your school is not different from the reported 17.8 hour benchmark when in fact it is different

C. Concluding that the mean number of hours studied at your school is different from the reported 17.8 hour benchmark when in fact it is not different

c. What is a Type II error for your​ test?

A. Concluding that the mean number of hours studied at your school is not different from the reported 17.8 hour benchmark when in fact it is different

B. Concluding that the mean number of hours studied at your school is different from the reported 17.8 hour benchmark when in fact it is different

C. Concluding that the mean number of hours studied at your school is different from the reported 17.8 hour benchmark when in fact it is not different

Solutions

Expert Solution

Part a

The null and alternative hypotheses for test are given as below:

Correct Answer: H

H0: µ = 17.8, H1: µ ≠ 17.8

The null and alternative hypotheses in words are given as below:

Null hypothesis: H0: Students studied an average of 17.8 hours.

Alternative hypothesis: H1: Students studied an average different from 17.8 hours.

Part b

Answer: C. Concluding that the mean number of hours studied at your school is different from the reported 17.8 hour benchmark when in fact it is not different.

Explanation:

We know that the type I error is the probability of rejecting the null hypothesis when it is true. For the given scenario, the type I error occurs when we reject the null hypothesis that students studied an average of 17.8 hours, in fact it is 17.8 hours.

Part c

Answer: A. Concluding that the mean number of hours studied at your school is not different from the reported 17.8 hour benchmark when in fact it is different.

Explanation:

We know that type II error occurs when we do not reject the null hypothesis when it is not true. For the given scenario, the type II error occurs when we do not reject the null hypothesis that students studied an average of 17.8 hours, in fact it is different from 17.8 hours.

milcah answered 3 weeks ago
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