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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=∑zxzy/(n-1)

where zxn=(xn-xmean) /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) /(n-2) =0.5/(1-0.25)/(3-2) =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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Most popular questions from this chapter

Following are the age and price data for custom homes, use α=0.01

presuming that the assumption for regression inference are met, decide at the specified significance level whether the data provide sufficient evidence to conclude that the predictor variable is useful for providing the response variable.

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