In a study testing whether 1 < 2 at the = 0.05 level of significance, the p-valu

Question

In a study testing whether 1 < 2 at the = 0.05 level of significance, the p-value was found to be 0.001. Assume that the populations are normally distributed, what is an appropriate conclusion to the test?        

A   Reject H0. There is sufficient evident at the = 0.05 level of significance to conclude that 1 < 2.

B   Reject H0. There is not sufficient evident at the = 0.05 level of significance to conclude that 1 < 2.

C   Do not reject H0. There is sufficient evident at the = 0.05 level of significance to conclude that 1 < 2.

D    Do not reject H0. There is not sufficient evident at the =0.05 level of significance to conclude that 1< 2.

Explanation / Answer

Solution

Correct answer is (A)

Explanations

p-value of a test is the probability that a test statistics (t) would take a value greater than or equal to the actual calculated value of the test statistics (tcal), when H0 is true.

i.e., p-value = P(t tcal/H0).

Relation Between p-value and Level of Significance

Level of significance, , is the pre-fixed level for Type I Error [Probability of rejecting H0, when H0 is true.] For a one-sided-right tail test, if t is the upper % point of the distribution of the test-statistics, then H0 is rejected if tcal > t. So, H0 is rejected if tcal is to the right of t which in turn implies that P(t tcal/H0) will be less than . Therefore, H0 is rejected if the p-value < level of significance.

In the given question, p-value (0.001) < level of significance. Hence, H0 is rejected ….. (1)

Now, in testing of hypothesis, the null hypothesis MUST always be in equality format. Thus, when we want to test if 1 < 2, our H0 is: 1 = 2 and HA is: 1 < 2 ………………….(2)

(1) and (2) => H0 is rejected implying that there is sufficient evidence at 5% level of significance that 1 < 2.

Now, to confirm other answer options are not correct,

(B) can be correct only if H0 is: 1 < 2, which is not permitted in testing hypothesis.

Since p-value < level of significance. H0 must be rejected. So, neither (C) nor (D) can be correct.

DONE

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