Question

Complete the statement. A critical value is​ _____________. Choose the correct answer below. A. A critical value is how far away our sample statistic can be from the true population parameter with a certain level of confidence. B. A critical value is the probability of obtaining a sample statistic like the one obtained from the sample or something more unusual if the null hypothesis is true. C. A critical value is the number of standard errors​ (or standard​ deviations) to move from the mean of a sampling distribution to correspond to a specified level of confidence. D. A critical value is the value that best estimates a population parameter.

Answer 1

A. A critical value is how far away our sample statistic can be from the true population parameter with a certain level of confidence.

Explanation:

Test of a hypothesis:

When we are testing a hypothesis, we have a null hypothesis and an alternative hypothesis, and the conclusion depends on the test statistic, given by:

`z = (X - \mu)/((\sigma)/(√(n)))`

In which X is the sample mean,
`\mu` is the value tested at the null hypothesis,
`\sigma` is the standard deviation and n is the size of the sample.

The test statistic measures the number of standard errors that we have to move away from the sample mean, and the critical value is how much we can be far from the population parameter with a certain level of confidence, that is, before a certain value we do not reject the null hypothesis, after the value we reject, and this value is the critical value, and thus the correct answer is given by option a.