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

Question

4. 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) = 0 + 1x, to the data below. Is there sufficient evidence (at = 0.10) of a positive linear relationship between y and x?
School         Annual tuition ($)               % with Job Offer

1                      39,662                                  93
2                      39,611                                  84
3                      39,479                                  96
4                      39,065                                  94
5                      38,979                                  89
6                      37,922                                  94
7                      37,241                                  92
8                      37,002                                  88
9                      36,466                                  98
10                     36,019                                  83
Give the null and alternative hypotheses for testing whether there exists a positive linear
relationship between y and x?
A.   H0: 0 = 0 Ha: 0 0
C. H0: 0 = 0 Ha: 0 < 0
E.   H0: 0 = 0 Ha: 0 > 0
B.   H0: 1 = 0 Ha: 1 0
D. H0: 1 = 0 Ha: 1 < 0
F.   H0: 1 = 0 Ha: 1 > 0

Find the test statistic.

t=_________ (Round to two decimal places as needed.)

Find the   p-value.
p-value =__________ (Round to four decimal places as needed.)
Make the appropriate conclusion at = 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. Reject H0. There is insufficient evidence that there exists a positive linear relationship between y and x.
C. Do not reject H0. There is sufficient 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.

Explanation / Answer

using R-software the following information is generated

Residuals:
Min 1Q Median 3Q Max
-7.749 -2.563 1.264 2.872 7.643

Coefficients:
Estimate Std. Error t-value Pr(>|t|)
(Intercept) 7.423e+01 4.809e+01 1.544 0.161
tuition 4.423e-04 1.260e-03 0.351 0.735

Residual standard error: 5.238 on 8 degrees of freedom
Multiple R-squared: 0.01517, Adjusted R-squared: -0.1079
F-statistic: 0.1232 on 1 and 8 DF, p-value: 0.7346

(first part) right choice is B.   H0: 1 = 0 Ha: 1 0

(second part) t-statistic, t=estimate/std.error=0.351

(third part) p-value=0.735

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

as the p-value=0.735 is more than alpha=0.1

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