If P = 0.016, which of the following is the best conclusion?
a. The probability that H0 is true is 0.016.
b. The probability that H0 is false is 0.016.
c. If H0 is false, the probability of obtaining a test statistic as extreme as or more extreme than the one actually observed is 0.016.
d. If H0 is true, the probability of obtaining a test statistic as extreme as or more extreme than the one actually observed is 0.016.
To determine the best conclusion, we need to understand the meaning of the given probability value, P = 0.016.
In hypothesis testing, the probability value (P-value) represents the likelihood of obtaining a test statistic as extreme as or more extreme than the one actually observed, assuming that the null hypothesis (H0) is true.
Now, let's analyze the given options:
a. The probability that H0 is true is 0.016.
This conclusion is incorrect because the P-value does not directly represent the probability of the null hypothesis being true. It only indicates the probability of obtaining the observed result assuming the null hypothesis is true.
b. The probability that H0 is false is 0.016.
This conclusion is also incorrect because the P-value does not directly represent the probability of the null hypothesis being false. It only provides information on the likelihood of obtaining the observed result assuming the null hypothesis is true.
c. If H0 is false, the probability of obtaining a test statistic as extreme as or more extreme than the one actually observed is 0.016.
This conclusion is incorrect because it reverses the logic. The correct interpretation is that if the null hypothesis is true, the probability of obtaining a test statistic as extreme as or more extreme than the one actually observed is 0.016.
d. If H0 is true, the probability of obtaining a test statistic as extreme as or more extreme than the one actually observed is 0.016.
This conclusion is the best among the given options. Based on the information provided, the P-value represents the probability of obtaining a test statistic as extreme as or more extreme than the one actually observed, assuming that the null hypothesis is true.
In summary, the best conclusion is option d: If H0 is true, the probability of obtaining a test statistic as extreme as or more extreme than the one actually observed is 0.016.