Question

listed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. alfa= 0.05. overhead width. 7.2 , 7.6 , 9.7 , 9.2 , 8.6 , 8.4 . weight. 119, 185, 246, 194, 194, 193. 1. determine the null and alternative hypotheses. 2.find the value of linear correlation r. 3. find the p-value of r. 4. find the test statistic. 5 conclusion (accept or reject ho) please show how do in the calculator ti-83.

Answer 1

1. Let the null and alternative hypotheses be H0 and H1 respectively. We have to test, H0: = 0 against H1: 0.

The linear correlation co-efficient is, r = 0.8712.

The test-statistic is, T = , where, r = 0.8712, n = 6.

Thus, T = 3.5492.

Under H0, T ~ t-distribution with (n-2) d.f. i.e. 4 d.f.

The p-value = 2 * P(T > 3.5492) = 2 * 0.0119 = 0.0238.

Since, p-value < level of significance = 0.05, we reject H0 and conclude that the correlation is significant.