Question

A researcher comparing two groups obtains a p-value of .19. The probability of getting:

1)the obtained test statistic is .19 if the null hypothesis is true

2) the obtained test statistic is .19 if the alternative hypothesis is true

3) a test statistic as extreme or more extreme than the obtained test statistic is .19 if the null hypothesis is true

4) a test statistic as extreme or more extreme than the obtained test statistic is .19 if the alternative hypothesis is true

Answer 1

A p-value of .19 indicates that there is a 19% probability of obtaining a test statistic as extreme or more extreme than the observed one if the null hypothesis is true, making it not statistically significant against a typical alpha level of 0.05.

Step-by-step explanation:

When a researcher comparing two groups obtains a p-value of .19, it indicates the probability of obtaining a test statistic as extreme or more extreme than the one observed if the null hypothesis is true. Specifically:

1. The probability of getting the obtained test statistic is .19 if the null hypothesis is true.
2. The probability of getting the obtained test statistic is not determined by the p-value if the alternative hypothesis is true.
3. The probability of getting a test statistic as extreme or more extreme than the obtained test statistic is .19 if the null hypothesis is true.
4. Similar to the second point, the p-value does not determine the probability of a test statistic as extreme if the alternative hypothesis is true.

It is important to note that a p-value of .19 is considered not statistically significant if we are using a common alpha level of 0.05 (5 percent), implying that we would not reject the null hypothesis based on this p-value.