Question

include twst statistic and critical values

10.1.5 Question Help H Fifty-four wild bears were anesthetized, and then their weights and chest seres were measured and listed in a dataset. Results Correlation Results are shown in the accompanying display. Is there sufficient evidence to support the claim that there is a linear correlation between Correlation coeff, r: 0954969 the weights of bears and their chest sizes? When measuring an anestheticed bear, is it easier to measure chest size than Critical weight? If so, does it appear that a measured chest size can be used to predict the weight? Use a significance level of a=0.05 +0.2680855 P-value (two tailed: 0.000 Determine the null and alternative hypotheses Hop V H₂ :P (Type integers or decimals. Do not round.) 0

Answer 1

The researcher wants to check the claim that there is linear correlation between the weights of bears and their chest sizes.

The sample size (n) is 54.

The given results are,

Correlation coefficient (r)	0.954969
Critical r:	± 0.2680855
p-value (two-tailed)	0.000

The null and the alternative hypothesis:

Но :p 0 HP +0

The test is two-tailed.

Test statistic:

$t = \frac{{r\sqrt {n - 2} }}{{\sqrt {1 - {r^2}} }} = \frac{{\left( {0.954969} \right)\sqrt {54 - 2} }}{{\sqrt {1 - {{\left( {0.954969} \right)}^2}} }} = 23.2095$

Thus, the value of test statistic 23.2095.

The degrees of freedom is n – 2 = 54 – 2 = 52

At the significance level 0.05 and the degrees of freedom 52, the two tailed critical value (r_c) is ± 0.2680855.

Since, the test statistic (23.2095) is greater than the critical value (0.2680855), so the researcher rejects the null hypothesis.

Therefore, it can be concluded that there is a sufficient evidence to support the researcher’s claim that there is linear correlation between the weights of bears and their chest sizes.