Animal researchers studying cows and horses conducted a two-sample t-test for a difference in means to investigate whether grazing cows eat more grass, on average, than grazing horses. All conditions for inference were met, and the test produced a test statistic of t=1.064 and a P-values of 0.0487 Which of the following is a correct interpretation of the P-value? A. The probability that cows eat more grass than horses, on average, is 0.0487.
B. The probability that cows eat the same amount of grass as horses, on average, is 0.0487
C. Assuming that the mean amount of grass eaten by cows is greater than the mean amount of grass eaten by horses, the probability of observing a test statistic of at most 1.664 is 0.0487.
D. Assuming that the mean amount of grass eaten by cows is equal to the mean amount of grass eaten by horses, the probability of observing a test statistic of at most 1.664 is 0.0487.
E. Assuming that the mean amount of grass eaten by cows is equal to the mean amount of grass eaten by horses, the probability of observing a test statistic of at least 1.664 is 0.0487.

If the null is true in this scenario, then the probability of observing a test statistic of at least 1.664 is 0.0487.

In null hypotheses, there is no relationship between the two phenomenons under the assumption or it is not associated with the group. And in alternative hypotheses, there is a relationship between the two chosen unknowns.

Test statistics, t = 1.064

P-value = 0.0487

The null hypothesis will be

H₀: μ₁ = μ₂ (There is no difference in the mean number of grass eaten by cows and horses)

An alternative hypothesis will be

Hₐ: μ₁ > μ₂

The null is assumed true unless tested otherwise, the P-value is used as a probability metric for the rejection or acceptance of the null.

Therefore, if the null is true in this scenario, then the probability of observing a test statistic of at least 1.664 is 0.0487.

More about the null hypotheses and alternative hypotheses link is given below.

link

E. Assuming that the mean amount of grass eaten by cows is equal to the mean amount of grass eaten by horses, the probability of observing a test statistic of at least 1.664 is 0.0487

Step-by-step explanation:

Given that :

Test statistic, t = 1.064

P-value = 0.0487

Hypothesis : To test if grazing cows eat more grass than grazing horses

The null hypothesis will be :

H0 : μ1=μ2(that is there is no difference on the mean number of grass eaten by cows and horses).

Alternative hypothesis ; H1 : μ1 > μ2

The null is assumed true unless tested otherwise, the P-value is used as a probability metric for the rejection or acceptance of the null.

Therefore, if the null is True in this scenario, then, the probability of observing a test statistic of at least 1.664 is 0.0487