Question

If you pay more in tuition to go to a top business​school, will it necessarily result in a higher probability of a job offer at​ graduation? Let y=percentage of graduates with job offers and x=tuition ​cost; then fit the simple linear​ model, E(y)=β0+β1x​, to the data below. Is there sufficient evidence​ (at α=0.05) of a positive linear relationship between y and​ x?

School	Annual tuition​ ($)	​% with Job Offer
1	39,746	95
2	39,493	94
3	38,992	89
4	38,869	89
5	38,848	85
6	38,277	86
7	37,838	91
8	37,663	92
9	37,573	86
10	37,013	87

Give the null and alternative hypotheses for testing whether there exists a positive linear relationship between y and​ x?

A.H0​: β0=0

Ha​:β0≠0

B.H0​: β1=0

Ha​:β1≠0

C.H0​: β0=0

Ha​: β0>0

D.H0​: β0=0

Ha​: β0<0

E.H0​: β1=0

Ha​: β1<0

F.H0​: β1=0

Ha​:β1>0

Find the test statistic.

t=_________

​(Round to two decimal places as​ needed.)

Find the​ p-value.

​p-value=_________

​(Round to four decimal places as​ needed.)

Make the appropriate conclusion at α=0.05.

Choose the correct answer below.

A.Reject H0. There is sufficient evidence that there exists a positive linear relationship between y and x.

B.Do not reject H0. There is sufficient evidence that there exists a positive linear relationship between y and x.

C.Do not reject H0. There is insufficient evidence that there exists a positive linear relationship between y and x.

D.Reject H0. There is insufficient evidence that there exists a positive linear relationship between y and x.

Answer 1

from above:

F.H0​: β1=0

Ha​:β1>0

test statistic t =1.60

p value =0.0741 (please try 0.0744 if this comes wrong)

C.Do not reject H0. There is insufficient evidence that there exists a positive linear relationship between y and x.