Question

explain what a p - value is. what is the criterion for rejecting the null hypothesis using the p - value approach? explain what a p - value is. choose the correct answer below a. a p - value is the probability of observing a sample statistic as extreme or more extreme than the one observed under the assumption that the statement in the null hypothesis is true. b. a p - value is the number of standard deviations that the observed proportion is from the proportion stated in the null hypothesis. c. a p - value is the value used to designate the area α in either the left - or right - tail of the normal curve. what is the criterion for rejecting the null hypothesis using the p - value approach? choose the correct answer below a. if p - value < - z_α for a left - tailed test, or if p - value > z_α for a right - tailed test, or if p - value < - z_{α/2} or p - value > z_{α/2} for a two - tailed test, then reject the null hypothesis. b. if p - value < α, reject the null hypothesis. c. if p - value > α, reject the null hypothesis.

Explanation:

The P - value is a fundamental concept in hypothesis testing. It represents the probability of obtaining a sample statistic as extreme or more extreme than the observed one, assuming the null hypothesis is true. This is a key definition in statistical hypothesis testing.

For the criterion of rejecting the null hypothesis using the P - value approach, the general rule is based on comparing the P - value with the significance level ($\alpha$). If the P - value is less than $\alpha$, it means that the observed result is unlikely to have occurred by chance under the null hypothesis, so we reject the null hypothesis.

Answer:

For the definition of P - value: A. A P - value is the probability of observing a sample statistic as extreme or more extreme than the one observed under the assumption that the statement in the null hypothesis is true.

For the criterion of rejecting the null hypothesis: B. If P - value < $\alpha$, reject the null hypothesis.