or a sample of eight bears, researchers measured the distances around the bears\

Question

or a sample of eight bears, researchers measured the distances around the bears' chests and weighed the bears. Mintab was used to find that the vakue of the inear comelation coefficient is r n 826 Using 1- 0 05, desermine if there is a inear correlaion between chest size and weight What proportion of the varlation in weight can be expltauned try the inear relationship between weight and chest size? ick here to view a table at crtsal vabies foe the corrclation.cocmcient is there a inear correlation between chest size and weight? MA. Yes, because the absolute value of the test statistic exeeds the crnical value of 0.707 B No, because the absoute value at the test statistic exceeds the crtical value of a 707 O c. Yes, because the test statstic falls between the cro al values: o 707 and 0 707. D. The answer cannot be determined from the given information b. What proportion of the variation in weight can be explaned by the inear relationshp between weight and chest sze? D:Round to three decimal places as needed) Enter your answer in the answer box and then click Check Answer ll arts showing Clear All

Explanation / Answer

(a) The null hypothesis is there is no linear correlation between size and weight

The critical value of Pearson Correlation coefficient with 8 degrees of freedom at alfa = 0.05 is 0.707

Since r= 0.826 > critical value

We reject the null hypothesis

So we conclude that there is linear correlation between size and weight

So answer is (A)

(b) r^2 = 0.68228

That is 68.228% of the variation in weight can be explained by the linear relationship between size and weight

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