The personal director of an engineering company believes that there is a significant positive correlation between the distance (in miles) an employee travels to work, *x*, and the number of minutes per month the employee is late, *y*. The sample data from a random sampling of 10 employees is shown in the table below. Is the personal director correct? Use α = 1%.
x 5 8 17 23 27 30 36 39 46 50
y 2 6 3 4 4 3 9 6 12 7
(a) State the hypotheses:
*H*<sub>0</sub>: The Select an answer
Select an answer
of miles traveled to work and minutes late per month
Symbols: Ο μ<sub>1</sub> - μ<sub>2</sub> Ο ρ Ο μ<sub>D</sub> Ο μ<sub>1</sub> - μ<sub>2</sub> Ο x̄ Ο μ<sub>0</sub> μ<sub>1</sub> - μ<sub>2</sub> ?
*H*<sub>a</sub>: The Select an answer
Select an answer
of miles traveled to work and minutes late per month
Symbols: Ο μ<sub>1</sub> - μ<sub>2</sub> Ο ρ Ο μ<sub>D</sub> Ο x̄ Ο μ<sub>0</sub> μ<sub>1</sub> - μ<sub>2</sub> ?
(b) State the decision rule:
Select an answer
at α =
is Select an answer
(c) Experiment:
Symbol of the sample statistic:
Ο x̄ Ο p̂<sub>1</sub> - p̂<sub>2</sub> Ο *r*
Ο p̂ Ο χ<sup>2</sup> Ο *p*
Ο x̄<sub>1</sub> - x̄<sub>2</sub> Ο μ<sub>D</sub> Ο μ<sub>p</sub>
Ο μ<sub>1</sub> - μ<sub>2</sub> Ο μ
Value of the sample statistic rounded to 2 decimal places:
% if the p-value of the Select an answer
P-value of the sample statistic rounded to 4 decimal places:
(d) Conclusion: Select an answer
at α =
%
(e) Answer the question: Is the personal director correct?
O Yes, because the p-value is less than alpha.
O No, because the p-value is less than alpha.
O No, because p-value is greater than alpha.
O Yes, because the p-value is greater than alpha.