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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 equals percentage of graduates with job offers and x equals tuition cost; then fit the simple linear model, E(y) = B0 + B1 * x , to the data below. Is there sufficient evidence (at alpha = 0.10 )  of a positive linear relationship between y and x?

School Annual_tuition ($) %_with_Job_Offer
1 39673 92
2 39517 81
3 39301 93
4 39166 96
5 38429 88
6 38359 91
7 37608 96
8 36888 96
9 36484 82
10 36282 89

other Questions included;

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

b) Find the test statistic.  and the P - value

c)

Make the appropriate conclusion at alpha = 0.10. 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. Reject H0. There is insufficient evidence that there exists a positive linear relationship between y and x.
D.Do not reject H0.There is insufficient evidence that there exists a positive linear relationship between y and x.

 

 

 

This question is a test of hypothesis conducted that should be conducted to evaluate the significance of the slope parameter. And the null hypothesis should be a right-tailed test because the question specifies that the association expected is a positive relationship. 

Therefore;- H0: b1 = 0 , and Ha: b1 > 0

The test statistic. 

Regression Statistics          
Multiple R 0.067          
R Square 0.004          
Adjusted R Square -0.120          
Standard Error 5.801          
Observations 10          
             
ANOVA            
  df SS MS F Significance F  
Regression 1 1.209 1.209 0.036 0.854  
Residual 8 269.191 33.649      
Total 9 270.400        
             
  Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept 79.495 57.557 1.381 0.205 -53.233 212.223
Annual_tuition ($) 0.000 0.002 0.190 0.854 -0.003 0.004

The test statistic is obtained from the regression summary table;- t = 0.190

  And the p-value is 0.854/2 = 0.427 

Correct conclusion based on the p-value method, 

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

 

 

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