$$\begin{array}{l}
\text { The western city wishes to see if there is a relationship between the summer temperature and the amount }\
\begin{array} { c c c }
& \left. \operatorname { Temp } ^ { \circ } { } ^ { \circ } \mathrm { C } \right) & \text { Kilowatts, } { } ^ { y } \
& 22.7 & 680 \
& 25.5 & 760 \
& 29.4 & 910 \
& 36.6 & 1,510 \
& 38.8 & 1,170 \
& 27.2 & 837 \
\text { of electricity used (in kilowatts). } & 24.4 & 600 \
& 40.5 & 1,800
\end{array}
\end{array}$$
-If a correlation coefficient calculated for n = 14 and $\alpha = 0.01$ is found to be r = 0.856, what is the test value for the t - test?
A) 4.059
B) 5.736
C) 2.851
D) 6.374

Question

$$\begin{array}{l}
\text { The western city wishes to see if there is a relationship between the summer temperature and the amount }\
\begin{array} { c c c } 
& \left. \operatorname { Temp } ^ { \circ } { } ^ { \circ } \mathrm { C } \right) & \text { Kilowatts, } { } ^ { y } \
& 22.7 & 680 \
& 25.5 & 760 \
& 29.4 & 910 \
& 36.6 & 1,510 \
& 38.8 & 1,170 \
& 27.2 & 837 \
\text { of electricity used (in kilowatts). } & 24.4 & 600 \
& 40.5 & 1,800
\end{array}
\end{array}$$
-If a correlation coefficient calculated for n = 14 and $\alpha = 0.01$ is found to be r = 0.856, what is the test value for the t - test?
A) 4.059
B) 5.736
C) 2.851
D) 6.374

Quizplus · Accepted Answer

The test value for the t-test is calculated using the formula: 
$$t = \frac{r\sqrt{n-2}}{\sqrt{1-r^2}}$$
Substituting the values given in the question, we get: 
$$t = \frac{(0.856)\sqrt{14-2}}{\sqrt{1-(0.856)^2}} \approx 5.736$$
Since we are given an alpha level of 0.01, the critical t-value can be found using a t-distribution table with 12 degrees of freedom (n-2). The critical t-value for a two-tailed test with alpha = 0.01 and 12 degrees of freedom is approximately 3.106. Since the calculated t-value of 5.736 is greater than the critical t-value of 3.106, we can reject the null hypothesis and conclude that there is a significant correlation between summer temperature and electricity usage in the western city.

-If a Correlation Coefficient Calculated for N = 14 And is