A policeman believes that the more text messages drivers send while driving, the greater the likelihood of being in a car accident. Which of the following findings would support his belief? a) r(30) = .38, p < .05
b) r(40) = .28, p < .01
c) r(30) = -.38, p < .05
d) r(40) = -.28, p > .05

The correct option is (a).

Step-by-step explanation:

The correlation coefficient is a statistical degree that computes the strength of the linear relationship amid the relative movements of the two variables (i.e. dependent and independent).It ranges from -1 to +1.

In this case, a hypothesis test for a significant positive correlation is to be performed to determine whether the claim made by the policeman is true or not.

The hypothesis can be defined as follows:

H₀: There isn't a positive correlation between the number of text messages drivers send while driving and the likelihood of being in a car accident, i.e. ρ ≤ 0.

Hₐ: There is a positive correlation between the number of text messages drivers send while driving and the likelihood of being in a car accident, i.e. ρ > 0.

Consider the first option.

The sample correlation computed from 30 samples data is,

r = 0.38

The correlation is positive and the sample size is large enough to rely on the  sample data.

The p-value of the test is, p < 0.05.

As the p-value is less than 5% level of significance, the null hypothesis will be rejected.

Thus, concluding that there enough evidence to support the policeman's belief.

Thus, the correct option is (a).

a is the correct