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

Ha : $p>0$is not rejected

Step-by-step solution

Correlation Coefficient 

Sample correlation coefficientr is calculated :$r=\sum _{}zxzy/(n-1)$

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

Using excel and above formula concept , $r=0.8771$

Hypothesis Testing 

r positive () for sample needs to be tested using hypothesis testing, to ensure that the population correlation parameter p(rho) is positive

$t=r/\sqrt{(1-r^2)\hspace{0.17em}/(n-2)}$

Putting $r=0.8771,andn=4,n-2=2$

We get $t=2.5$, which is greater than the tabulated t value at $0.05$significance level, and so $p$is less at same significance level.

Hence, we reject the null hypothesis in favour of alternate hypothesis.