True or False: When testing a hypothesis using the Classical A...

Question

True or False: When testing a hypothesis using the Classical Approach, if the sample proportion is too many standard deviations from the proportion stated in the null hypothesis, we reject the null hypothesis.

Accepted Answer

Welcome back everyone. In this problem, consider testing a hypothesis about a population proportion using the classical approach. Which statement is most accurate? A says to reject the null hypothesis when the test statistic Z falls in the rejection region determined by the chosen significance level alpha. B says to reject the null hypothesis when the sample proportion is farther from the population proportion than one divided by the square root of n, the sample size, regardless of alpha. She says we fail to reject the null hypothesis whenever the sample proportion is equal to the population proportion, even if the sample size n is enormous, and the D says to reject the null hypothesis only if the sample proportion is greater than the population proportion regardless of the alternative hypothesis. Now, since we're considering this test using the classical approach, let's try to ask ourselves, what do we know about this approach and how it can help us. Well, recall that in the classical approach we were comparing the test statistic often a Z score to critical values determined by the significance level. In other words, by definition, in the classical approach. OK, usually. We would reject the null hypothesis, if the calculated, if the calculated test statistic. OK, falls into the rejection region. OK. That's set by the significance level alpha. In other words, usually we would have our distribution, OK? And then we have our critical value and basically if this shaded area is our rejection region, then if our test statistic falls here, we would reject another hypothesis, but if it does not, OK. If it does not, let me just shade this in red to represent our rejection here, OK? But if it does not, then usually we do not reject or no hypothesis, OK? And it all depends again on our critical value for a test statistics. So if it's a Z score, then we'd find a critical Z value. So if we think about it here, based on this definition, it closely matches or it matches exactly a reject the null hypothesis when the test statistic falls in the rejection region determined by the chosen alpha. Thus, A is the correct answer. We can make sure we're right by considering the rest of options. In B, it says that we reject it when the sample proportion is farther from the population proportion than one divided by the square root of the sample size. What what is this value? Have you ever seen this before? This is just some arbitrary condition instead of the test statistic and alpha. So B would be incorrect. C says we fail to reject the null hypothesis when the sample proportion equals the population proportion. Even if the sample size n is enormous, no, while if both of the proportions are equal leads to failing to reject the null hypothesis, this only describes one specific improbable scenario and doesn't state the general decision rule that we considered in option A. So that's how we know C would be incorrect. And know for us to indeed where it says to reject on our hypothesis only if the sample proportion is greater than the population proportion without considering the alternative hypothesis would be an error because rejection depends on the alternative hypothesis we have to consider it. Having the sample proportion greater than the population proportion is only the rejection direction for a right-tailed test. So that's how we know D is also incorrect. Therefore, we're sure that A is the correct answer. Thanks a lot for watching everyone. I hope this video helped.

True or False: When testing a hypothesis using the Classical Approach, if the sample proportion is too many standard deviations from the proportion stated in the null hypothesis, we reject the null hypothesis.

Key Concepts

Classical Approach to Hypothesis Testing

Sample Proportion and Null Hypothesis Proportion

Standard Deviations and Rejection Criteria

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