Chpt 8

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

null

Which of the following is NOT a true statement about error in hypothesis​ testing? A. A type I error is making the mistake of rejecting the null hypothesis when it is actually false. B. A type II error is making the mistake of failing to reject the null hypothesis when it is actually false. C. A type I error is making the mistake of rejecting the null hypothesis when it is actually true. D. The symbol alphaα represents the probability of a type I error.

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

Which of the following is NOT true of using the binomial probability distribution to test claims about a​ proportion? Choose the correct answer below. A. One requirement of this method is that np>5 and nq>5. B. In a​ right-tailed test, the​ P-value is the probability of getting x or more successes among the n trials. C. In a​ left-tailed test, the​ P-value is the probability of getting x or fewer successes among the n trials. D. This method uses the binomial probability distribution with the​ P-value method and uses the value of p assumed in the null hypothesis.

A. One requirement of this method is that np>5 and nq>5.

Which of the following is NOT a requirement of testing a claim about a population proportion using a formal method of hypothesis​ testing? A. 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. B. The conditions for a binomial distribution are satisfied. C. The conditions np>5 and nq>5 are both satisfied. D. The sample observations are a simple random sample.

A. 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 true when testing a claim about a standard deviation or​ variance? A. The​ P-value method and the classical method are not equivalent to the confidence interval method in that they may yield different results. B. The condition of a normally distributed population is a much stricter requirement for the χ2 test than for the t test or the z test. C. The table for finding​ P-values does not usually give exact​ P-values as it only includes select values ofα and selected numbers of degrees of freedom. D. The χ2 test is not robust against a departure from normality.

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

Identify the type I error and the type II error that correspond to the given hypothesis. The percentage of adults who retire at age 65 is less than 62 %. Identify the type I error. Identify the type II error. A. Fail to reject the null hypothesis that the percentage of adults who retire at age 65 is less than 62% when the percentage is actually equal to 62%. B. Reject the null hypothesis that the percentage of adults who retire at age 65 is equal to 62% when that percentage is actually equal to 62 %. C. Fail to reject the null hypothesis that the percentage of adults who retire at age 65 is equal to 62 % when that percentage is actually less than 62 % D. Reject the null hypothesis that the percentage of adults who retire at age 65 is less than 62% hen that percentage is actually less than 62%

B and C

Which of the following is NOT a criterion for making a decision in a hypothesis​ test? A. If a confidence interval does not include a claimed value of a population​ parameter, the decision is to reject the null hypothesis. B. 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. C. If the test statistic falls within the critical​ region, the decision is to reject the null hypothesis. D. If ​P-valueless than or equals≤alphaα​, the decision is to reject the null hypothesis.​ Otherwise, we fail to reject the null hypothesis.

B. 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.

Which of the following is NOT a property of the​ chi-square distribution? A. The​ chi-square distribution is different for each number of degrees of​ freedom, df=n− 1. B. The mean of the​ chi-square distribution is 0. C. The values of​ chi-square can be zero or​ positive, but they cannot be negative. D. The​ chi-square distribution is not symmetric.

B. The mean of the​ chi-square distribution is 0.

Which of the following is not a requirement for testing a claim about a population with σ not​ known? A. The value of the population standard deviation is not known. B. The population​ mean, u​, is equal to 1. C. The sample is a simple random sample. D. Either the population is normally distributed or n>30 or both.

B. The population​ mean, u​, is equal to 1.

Which of the following is NOT a requirement for testing a claim about a population mean with σ ​known? A. The sample is a simple random sample. B. The sample​ mean, x is greater than 30. C. Either the population is normally distributed or n>30 or both. D. The value of the population standard deviation is known.

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

Which of the following is not true when using the confidence interval method for testing a claim about muμ when sigmaσ is​ unknown? Choose the correct answer below. A. For a​ one-tailed hypothesis test with a 0.05 significance​ level, one must construct a​ 90% confidence interval. B. The​ P-value method and the classical method are not equivalent to the confidence interval method in that they may yield different results. C. The​ P-value method, the traditional​ method, and the confidence interval method are equivalent and yield the same results. D. For a​ two-tailed hypothesis test with a 0.05 significance​ level, one must construct a​ 95% confidence interval.

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

Which of the following is NOT true about​ P-values in hypothesis​ testing? A. If the P is​ low, the null must go. B. The​ P-value separates the critical region from the values that do not lead to rejection of the null hypothesis. C. If the P is​ high, the null will fly. D. The​ P-value is an area.

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

Identify the type I error and the type II error that corresponds to the given hypothesis. The proportion of people who write with their left hand is equal to 0.24. Which of the following is a type I​ error? Which is type II error? A. Fail to reject the claim that the proportion of people who write with their left hand is 0.24 when the proportion is actually 0.24 B. Reject the claim that the proportion of people who write with their left hand is 0.24 when the proportion is actually different from 0.24. C. Reject the claim that the proportion of people who write with their left hand is 0.24 when the proportion is actually 0.24. D. Fail to reject the claim that the proportion of people who write with their left hand is 0.24 when the proportion is actually different from 0.24.

C and D

Which of the following is NOT true when testing a claim about a​ proportion? A. Both the traditional method and​ P-value method use the same standard deviation based on the claimed proportion​ p, but the confidence interval uses an estimated standard deviation based on the sample proportion ^p. B. If you want to test a claim about population​ proportions, use the​ P-value method or the classical method of hypothesis testing. C. A conclusion based on a confidence interval estimate will be the same as a conclusion based on a hypothesis test. D. When testing claims about population​ proportions, the traditional method and the​ P-value method are equivalent in the sense that they always yield the same result.

C. A conclusion based on a confidence interval estimate will be the same as a conclusion based on a hypothesis test.

Which of the following is NOT a requirement for testing a claim about a mean with σ ​known? A. If the sample results​ (or more extreme​ results) can easily occur when the null hypothesis is​ true, we attribute the relatively small discrepancy between the assumption and the sample results to chance. B. A conclusion based on a confidence interval estimate will be the same as a conclusion based on a hypothesis test. C. If the sample results​ (or more extreme​ results) cannot easily occur when the null hypothesis is​ true, we explain the discrepancy between the assumption and the sample results by concluding that the assumption is​ true, so we do not reject the assumption. D. If, under a given​ assumption, there is an exceptionally small probability of getting sample results at least as extreme as the results that were​ obtained, we conclude that the assumption is probably not correct.

C. If the sample results​ (or more extreme​ results) cannot easily occur when the null hypothesis is​ true, we explain the discrepancy between the assumption and the sample results by concluding that the assumption is​ true, so we do not reject the assumption.

Which of the following is NOT true about the tails in a​ distribution? A. The tails in a distribution are the extreme critical regions bounded by critical values. B. The critical region in a​ left-tailed test is in the extreme left tail. C. The inequality symbol in the alternative hypothesis points away from the critical region. D. The symbol not equals≠ is often expressed in computer science as​ <>, and this is a great reminder that an alternative hypothesis with the symbol not equals≠ corresponds to a two tailed test.

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

Which of the following is NOT a requirement for testing a claim about a standard deviation or​ variance? A. The​ chi-square distribution is used. B. The sample is a simple random sample. C. The population must be skewed to the right. D. The population has a normal distribution.

C. The population must be skewed to the right.

Which of the following is not a characteristic of the t​ test? A. The t test is robust against a departure from normality. B. The Student t distribution has the same general bell shape as the standard normal distribution. C. The Student t distribution is different for different sample sizes. D. The Student t distribution has a mean of t=0 and a standard deviation of s=1.

D. The Student t distribution has a mean of t=0 and a standard deviation of s=1.

Which of the following is not a strategy for finding​ P-values with the Student t​ distribution? A. Use a​ TI-83/84 Plus calculator to find the​ P-value rounded to at least 4 decimal places. B. Use the table in the book with the appropriate number of degrees of freedom to find a range of values containing the​ P-value. C. Use software such as​ Minitab, Excel, or STATDISK to find the​ P-value rounded to at least 4 decimal places. D. Use the table in the book to find the​ P-value rounded to at least 4 decimal places.

D. Use the table in the book to find the​ P-value rounded to at least 4 decimal places.

A​ _____________ is a procedure for testing a claim about a property of a population.

hypothesis test

The​ _________ of a hypothesis test is the probability ​(1-β​) of rejecting a false null hypothesis.

power

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