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Chapter 14: Q14.118 (page 585)

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

Short Answer

Expert verified

We accept the null hypothesis that variables are not linearly (positively) correlated.

Step by step solution

01

r calculation 

Sample correlation coefficientr is calculated : r=鈭�zxzy/(n-1)

where zxn=(xn-xmean)鈥�/standarddeviation, and same for zyn

Using excel and above formula concept , r = 0.5

02

Hypothesis Testing 

r positive ( r>0) for sample needs to be tested using hypothesis testing, to ensure that the population correlation parameter p(rho) is positive

t=r/(1-r2)鈥�/(n-2)鈥�=0.5/(1-0.25)/(3-2)鈥�=0.5/0.75=0.5/0.8660

=0.577

As calculated t value tabulated t at 0.10 significance level, so p value would be greater at the same significance level.

So, accept the null hypothesis and conclude that variables are not linearly correlated.

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