Question

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

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

Short answer

We reject the null hypothesis $Ha:\hspace{0.17em}p\ne 0$, the variables are not linearly correlated.

Step-by-step solution

Correlation Coefficient 

Sample correlation coefficient is calculated by

$r=\sum _{}zxzy/(\hspace{0.17em}n-1)\hspace{0.17em}$

where $z{x}_n=(x_{n-}xmean)/s\tan darddeviation$, and same for $z{y}_n$

Using excel and above, $r=-0.6325$

Hypothesis Testing 

$r\ne 0$for sample needs to be tested using hypothesis testing, to ensure that the population correlation parameterp (rho) $\ne 0$

$$\begin{gathered} t=r/\sqrt{(1-r^2)\hspace{0.17em}/(n-2)} \\ =-0.6325/\sqrt{0.599/3} \\ =-0.6325/0.4468 \\ t=-1.415 \end{gathered}$$

As t value is smaller and p value is greater at two sided 0.10 significance level, so we accept the null hypothesis $[H_0:\hspace{0.17em}p=0]$