Question

For each exercise, decide, at 10% significance level, whether the data provide sufficient evidence t reject the null hypothesis in favour of alternate hypothesis

Ha :$p<\hspace{0.17em}0$

Short answer

We don't reject Ha : $p<\hspace{0.17em}0$and state that variables are negatively linearly correlated

Step-by-step solution

Correlation Coefficient 

Sample correlation coefficientr is calculated :

where , and same for

Using excel and above formula concept ,r = -0.7559

Hypothesis Testing 

r negative $(r<\hspace{0.17em}0)$ for sample needs to be tested using hypothesis testing, to ensure that the population correlation parameter p(rho) is negative

$$\begin{gathered} t=-0.7559/\sqrt{(1-0.5714)\hspace{0.17em}/(3-2)\hspace{0.17em}} \\ t=-0.7559/\sqrt{0.4286} \\ t=-0.7559/0.6547 \\ t=-1.1546 \end{gathered}$$

As t calculated value is more than tabulated t value at 0.10 significance level, and p value at the same corresponding level = 0.454

So, we reject the null hypothesis that p = 0, and don't reject the alternate hypothesis that p < 0