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 yequalspercentage of graduates with job offers and xequalstuition ​cost; then fit the simple linear​ model, Upper E (y )equals beta 0 plus beta 1 x​, to the data below. Is there sufficient evidence​ (at alphaequals0.05​) of a positive linear relationship between y and​ x?

Answer 1

ANSWER

a. the test statistic t = (1.52 )

b. the​ p-value. p-value.= ( 0.1679 )

c. since p-value=0.1619 is more than the level of significance alpha=0.1 so

Don’t reject H0.Theren is insufficient evidence that there exists a positive linear relationship between y and x.

Explanation:

the linear model fitting analysis is given as

here null hypothesis H0:β1=0 and alternative hypotheis H1:β1≠0

Analysis of Variance

Source DF Sum of Squares Mean Square F Value Pr > F

Model 1 61.52564 61.52564 2.30 0.1679

Error 8 214.07436 26.75930

Corrected 9 275.60000

Total

Root MSE 5.17294 R-Square 0.2232

Dependent Mean 89.20000 Adj R-Sq 0.1261

Coeff Var 5.79926

Parameter Estimates

Variable DF Parameter Estimate Standard Error t Value Pr > |t|

Intercept 1 9.54781 52.55541 0.18 0.8604

tution 1 0.00208 0.00137 1.52 0.1679

ANSWER

a. the test statistic t = (1.52 )

b. the​ p-value. p-value.= ( 0.1679 )

c. since p-value=0.1619 is more than the level of significance alpha=0.1 so

Don’t reject H0.Theren is insufficient evidence that there exists a positive linear relationship between y and x.