Suppose you conduct a test and your p-value is equal to 0.016. what can you conclude?

Suppose you conduct a test and your p-value is equal to 0.016. What can you conclude?

A. Reject Ho at alpha=0.05 but not at alpha=0.10
B. Reject Ho at alpha=0.05 but not at alpha=0.01
C. Reject Ho at alpha=0.01 but not at alpha=0.05
D. Reject Ho at alpha=0.10 but not at alpha=0.05
E. Reject Ho at alpha equal to 0.10,0.05, and 0.01
F. Do not reject Ho at alpha equal to 0.10, 0.05, or 0.01

General guidance

Concepts and reason
Null hypothesis: The null hypothesis states that there is no difference in the test, which is denoted by . Moreover, the sign of null hypothesis is equal , greater than or equal and less than or equal .

Alternative hypothesis: The hypothesis that differs from the is called alternative hypothesis. This signifies that there is a significant difference in the test. The sign of alternative hypothesis is less than , greater than , or not equal .

P-value: The probability of getting the value of the statistic that is as extreme as the observed statistic when the null hypothesis is true is called as P-value.

Fundamentals

Rejection rule based on p-value:

If , then reject the null hypothesis.

If , then do not reject the null hypothesis.

Step-by-step

Step 1 of 2

From the given information, the p-value is 0.016.

Conclusion for .

Use the significance level, The is less than the level of significance.

That is, .

Therefore, by the rejection rule, reject the null hypothesis.

Conclusion for .

Use the significance level, The is greater than the level of significance.

That is, .

Therefore, by the rejection rule, do not reject the null hypothesis.

Conclusion for .

Use the significance level, The is less than the level of significance.

That is, .

Therefore, by the rejection rule, reject the null hypothesis.

Hence, the options (A), (C), (D), (E) and (F) are incorrect.

The p-value and the level of significance are compared to check if the null hypothesis is rejected or not. If p-value is greater than the level of significance then the null hypothesis is not rejected otherwise it is rejected.

Step 2 of 2

Conclusion for .

Use the significance level, The is greater than the level of significance.

That is, .

Therefore, by the rejection rule, do not reject the null hypothesis.

Conclusion for .

Use the significance level, The is less than the level of significance.

That is, .

Therefore, by the rejection rule, reject the null hypothesis.

Hence, the option (B) is correct.

Reject at but not at .

The p-value and the level of significance are compared to check if the null hypothesis is rejected or not. If p-value is greater than the level of significance then the null hypothesis is not rejected otherwise it is rejected.

Reject at but not at .