Question

Determine the null and alternative hypotheses на от (Type integers or decimals. Do not round) Identify the correlation coefficient, (Round to three decimal places as needed) Identify the critical value(s) (Round to three decimal places as needed OA. There are two critical values atr= O B. There is one critical value atra Is there sufficient evidence to support the claim that there is a linear correlation between the weights of bears and their chest sizes? Choose the correct answer below and, if necessary fill in the answer box within your choice (Round to three decimal places as needed O A. No, because the absolute value of the test statistic exceeds the critical value O B. Yes, because the absolute value of the test statistic exceeds the critical value OC. Yes, because the test statistic falls between the critical values OD No because the test statistic falls between the critical values O E The answer cannot be determined from the given information When measuring an anesthetized bear is it easier to measure chest size than weight? If so, does it appear that a measured chest size can be used to predict the weight? O A. No, it is easier to measure weight than chest size because the chest is not a flat surface OB. Yes, it is easier to measure a chest size than a weight because measuring weight would require lifting the bear onto the scale. The chest size could not be used to predict weight because there is not a linear correlation between the two OC. Yes, it is easier to measure a chest size than a weight because measuring weight would require lifting the bear onto the scale. The chest size could not be used to predict weight because there is too much variance in the weight of the bears. OD. Yes, it is easier to measure a chest size than a weight because measuring weight would require lifting the bear onto the scale. The chest size could be used to predict weight because there is a linear correlation belween the two Click to select your answer(s).

54 wild bears are anesthetized, and then their waits and chest sizes were measured and listed in a data set. Results are shown in the accompanying display. Is there sufficient evidence to support the claim that there is a linear correlation between the weights of bears and their chest sizes? When measuring an anesthetized bear, is it easier to measure chest size and weight? If so, does it appear that a measured chest size can be used to predict the weight? Use a significance level of alpha = 0.05.

Answer 1

The null and the alternative hypothesis are

$H_0: \rho=0 \\~~~~~ H_a: \rho \not=0$

From the result given the correlation coefficient is $r=0.962$

The critical values are $t=\pm 0.268$

Also value of test static $t= {r\sqrt{n-2}\over \sqrt{1-r^2}}={0.962\sqrt{54-2}\over \sqrt{1-(0.962)^2}} \approx 25.406$

Hence there is sufficient evidence to support the claim that there is a linear correlation between the two.

Option B is correct with t=25.406

Yes its easier to measure chest size than weight as there is linear correlation between the two

Option D) is correct