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Chapter 14: Q14.119 (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

Ha :p< 0

Short Answer

Expert verified

We don't reject Ha : p< 0and state that variables are negatively linearly correlated

Step by step solution

01

Correlation Coefficient 

Sample correlation coefficientr is calculated :

where , and same for

Using excel and above formula concept ,r = -0.7559

02

Hypothesis Testing 

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

t=-0.7559/(1-0.5714) /(3-2) t=-0.7559/0.4286t=-0.7559/0.6547t=-1.1546

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

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