Question

In: Statistics and Probability

If you pay more in tuition to go to a top business​ school, will it necessarily...

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).

Solutions

Expert Solution

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


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