chapter 8

Power

=1-type 2 error

Which of the following is NOT a true statement about error in hypothesis​ testing?

A type I error is making the mistake of rejecting the null hypothesis when it is actually false.

Identify the type II error. Choose the correct answer below.

Fail to reject the null hypothesis that the percentage of high school students whohigh school students who graduate is equal to %55% when that percentage is actually greater than %55%.

Fill in the blank. A​ _____________ is a procedure for testing a claim about a property of a population.

Hypothesis test

Which of the following is NOT a criterion for making a decision in a hypothesis​ test?

If the​ P-value is less than​ 0.05, the decision is to reject the null hypothesis.​ Otherwise, we fail to reject the null hypothesis.

Fill in the blank. The​ _________ hypothesis is a statement that the value of a population parameter is equal to some claimed value.

Null

Fill in the blank. The​ _________ of a hypothesis test is the probability ​(1−β​) of rejecting a false null hypothesis.

Power

Identify the type I error. Choose the correct answer below.

Reject the null hypothesis that the percentage of high school students whohigh school students who graduate is equal to %55% when that percentage is actually equal to %55%.

Fill in the blank. The​ ___________ is a value used in making a decision about the null hypothesis and is found by converting the sample statistic to a score with the assumption that the null hypothesis is true.

Test Statistic

Which of the following is NOT true about the tails in a​ distribution?

The inequality symbol in the alternative hypothesis points away from the critical region.

Which of the following is NOT a requirement of testing a claim about a population proportion using a formal method of hypothesis​ testing?

The lowercase​ symbol, p, represents the probability of getting a test statistic at least as extreme as the one representing sample data and is needed to test the claim.

Which of the following is not a requirement for testing a claim about a population with sigmaσ not​ known?

The population​ mean, μ​, is equal to 1.

Make a decision about the given claim. Use only the rare event​ rule, and make subjective estimates to determine whether events are likely. For​ example, if the claim is that a coin favors heads and sample results consist of 11 heads in 20​ flips, conclude that there is not sufficient evidence to support the claim that the coin favors heads​ (because it is easy to get 11 heads in 20 flips by chance with a fair​ coin). ​Claim: The mean ageage of students in a large mathmath class is lessless than 3333. A simple random sample of the students has a mean ageage of 32.432.4

The sample is notis not unusual if the claim is true. The sample is notis not unusual if the claim is false.​ Therefore, there is notis not sufficient evidence to support the claim.

Which of the following is NOT a requirement for testing a claim about a population mean with σ known?

The sample​ mean, x overbar x is greater than 30.

Which of the following is not a characteristic of the t​ test?

The t test is robust against a departure from normality.

Which of the following is not true when using the confidence interval method for testing a claim about μ when σ is​ unknown?

The​ P-value method and the classical method are not equivalent to the confidence interval method in that they may yield different results.

The Ericsson method is one of several methods claimed to increase the likelihood of a baby girl. In a clinical​ trial, results could be analyzed with a formal hypothesis test with the alternative hypothesis of p>​0.5, which corresponds to the claim that the method increases the likelihood of having a​ girl, so that the proportion of girls is greater than 0.5. If you have an interest in establishing the success of the​ method, which of the following​ P-values would you​ prefer: 0.999,​ 0.5, 0.95,​ 0.05, 0.01,​ 0.001? Why?

The​ P-value of 0.001 is preferred because it corresponds to the sample evidence that most strongly supports the alternative hypothesis that the method is effective.

Which of the following is NOT true about​ P-values in hypothesis​ testing?

The​ P-value separates the critical region from the values that do not lead to rejection of the null hypothesis.