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Chapter 14: Q. 14.123 (page 585)

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

Ha:蚁鈮�0

Short Answer

Expert verified

We reject the null hypothesis Ha:蚁鈮�0, the variables are not linearly correlated.

Step by step solution

01

Step 1. Correlation Coefficient 

Sample correlation coefficient is calculated by

r=鈭�zxzy/(鈥�n-1)鈥�

where, zxn=(xn-xmean)/standarddeviationand same for zyn

So,r=-0.6325

02

Step 2. Hypothesis Testing 

r鈮�0for sample needs to be tested using hypothesis testing, to ensure that the population correlation parameter蚁(rho)鈮�0

t=r/(1-r2)鈥�/(n-2)=-0.6325/0.599/3=-0.6325/0.4468t=-1.415

As tvalue is smaller and pvalue is greater at two sided 0.10significance level, so we accept the null hypothesis[H0:蚁=0]

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