# 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?

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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.