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Chapter 14: Q14.120 (page 585)

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

Ha :pnot=0.

x04312
y19843

Short Answer

Expert verified

We don't reject Ha : pnot=0, and state that the variables are linearly correlated.

Step by step solution

01

Correlation Coefficient 

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

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

Using excel and above formula concept,r=0.9325

02

Hypothesis Testing 

rnot=0for sample needs to be tested using hypothesis testing, to ensure that the population correlation parameterp (rho) is non zero.

t=r/(1-r2)鈥�/(n-2)0.9325/(1-0.9325)/(5-2)0.9325/0.0675/30.9325/0.02250.9325/0.15t=6.216

As t calculated value is greater than t value for 10%significance level ie 0.05each side, and p value =0.02is also lesser than p at the same significance level

So, we reject the null hypothesis H0 : p=0in favour of alternate hypothesis H1 : pnot=0. Hence, the variables are linearly correlated.

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