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 :$p\ne 0$

Short answer

$Ha:\hspace{0.17em}p\ne 0$ is rejected. The variables are not linearly correlated.

Step-by-step solution

Correlation Coefficient 

Sample correlation coefficient r is calculated by : $r=\sum _{}zxzy/(n-1)\hspace{0.17em}$

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

Using excel and above formula concept,$r=-0.7206$

Hypothesis Testing 

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

$$\begin{gathered} t=r/\sqrt{(1-r^2)\hspace{0.17em}/(n-2)\hspace{0.17em}} \\ -0.7206/\sqrt{0.4807/2} \\ -0.7206/0.4903 \\ t=-1.469 \end{gathered}$$

As t calculated value at 0.10 significance level is more that, and p value at the same significance level $=0.2794$is more

So, we accept the null hypothesis in $p=0$, and reject the null hypothesis.