As you may know, there has been bad blood between the Montague family and the Capulet family for a good while. In this modern day, resolution can be achieved by using a psychological test. In the test of "propensity to fall in love,"the mean of the 6 Montagues was 54 and the mean of the 10 Capulets was 64. (Italian norms show a national average of 100.) When a statistician compared the families with a t test, a value of 2.13 was obtained. If you adopt an $\alpha$ level of .05 (two-tailed test), you should conclude that the Capulets are
A) significantly more loving than the Montagues
B) significantly less loving than the Montagues
C) not significantly different from the Montagues
D) not yet comparable additional information is needed.

Question

Quizplus · Accepted Answer

The t-value of 2.13 is compared to the critical t-value for a two-tailed test with $\alpha$ = 0.05. With degrees of freedom calculated as 14 (6 Montagues + 10 Capulets - 2), the critical t-value is approximately 2.145. Since 2.13 is less than 2.145, the difference is not statistically significant.

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