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​ (α=0.10 of a positive linear relationship between y and​ x?

School	Annual tuition​ ($)	​% with Job Offer
1	39,738	95
2	39,301	86
3	39,182	92
4	38,731	98
5	38,497	98
6	38,254	91
7	37,946	91
8	37,794	98
9	36,734	91
10	36 comma 14836,148	8585

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

A.H0​: β1s=0

Ha​:β1<0

B. H0​: β0=0

Ha​:β<0

C.H0​: β0=0

Ha​:β0>0

D. HO: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-=______________ ​(Round to four decimal places as​ needed.)

Make the appropriate conclusion = ALPHA=0.10

Choose the correct answer below.

A.

Do not reject

H0. There is

insufficient

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.

Reject

H0.

There is

insufficienti

evidence that there exists a positive linear relationship between y and x.

D.

Reject

H0.

There is

sufficient

evidence that there exists a positive linear relationship between y and x.

Click to select your answer(s).

Answer 1

Given that

= 0.10

x = Tuition cost

y = Percentage of graduates with job offers

Simple linear model E(y)=β0+β1x

Here

Null hypothesis ,

Alternate Hypothesis ,

S.NO	X	Y	(X-)2	(Y-)2	(X-)(Y-)
1	39,738	95	2266530.25	6.25	3762.5
2	39,301	86	1141692.25	42.25	-6942
3	39,182	92	901550.25	0.25	-474.5
4	38,731	98	248502.25	30.25	2739
5	38,497	98	69960.25	30.25	1452
6	38,254	91	462.25	2.25	-31.5
7	37,946	91	82082.25	2.25	430.5
8	37,794	98	192282.25	30.25	-2414.5
9	36,734	91	2245502.25	2.25	2248.5
10	36,148	85	4345140.25	56.25	15637.5
Total	382,325	925	11493704.5	202.5	16407.5
Mean	38,233	92.5	SSX	SSY	SXY

Correlation Coefficient, r = SXY / (SSX*SSY) = 0.3400

Test statistic, t= r*sqrt(n-2) / sqrt(1-r²) = 1.02

P-value = 0.1688 (Round to four decimals)

Here, P-value is greater than 0.10 significance level we do not reject null hypothesis and can conclude that there is insufficient evidence that there exists a positive relationship between X and Y

Option A