chapter 8

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. Your answer is correct. B.The symbol alphaα represents the probability of a type I error. C.A type II error is making the mistake of failing to reject the null hypothesis when it is actually false. D.A type I error is making the mistake of rejecting the null hypothesis when it is actually true.

critical value

a test statistic value beyond which we reject the null hypothesis; often called a cutoff

Hypothesis

claim or statement about a property of a population

null hypothesis

contains a condition of equality

p-value>alpha

fail to reject Ho

type 2 error

failing to reject a false null hypothesis

significance level

if not selected for you then it's 0.05.

A hypothesis test

is a procedure for testing a claim about a property of a population

The null hypothesis

is a statement that the value of a population parameter is equal to some claimed value.

alternative hypothesis

must not contain condition of equality

p-value < alpha

reject the null hypothesis

hypothesis test- test of significance

standard procedure for testing a claim about a property of a population

The rare event rule

states that​ if, under a given​ assumption, the probability of a particular observed event is extremely​ small, we conclude that the assumption is probably not correct.

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

requirements for testing claims about population proportion p

1. sample observations are a simple random sample 2. the conditions for a binomial distribution are satisfied. 3. condition np and nq greater than 5 so binomial distribution of the sample proportion can be approximated by normal distribution with mu=np and sigma=squareroot npq

common methods for testing claim about population

1. use normal distribution as an approximation to binomial distribution 2. use an exact method based on the binomial probability distribution

Which of the following is NOT true when testing a claim about a​ proportion?

A conclusion based on a confidence interval estimate will be the same as a conclusion based on a hypothesis test. This is the correct answer. B.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.If you want to test a claim about population​ proportions, use the​ P-value method or the classical method of hypothesis testing. D.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 ModifyingAbove p with caretp.

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

C.The inequality symbol in the alternative hypothesis points away from the critical region. This is the correct answer.

Which of the following is NOT true of using the binomial probability distribution to test claims about a​ proportion?

A. One requirement of this method is that np>5 and nq>5. This is the correct answer. B.In a​ left-tailed test, the​ P-value is the probability of getting x or fewer successes among the n trials. C.This method uses the binomial probability distribution with the​ P-value method and uses the value of p assumed in the null hypothesis. D.In a​ right-tailed test, the​ P-value is the probability of getting x or more successes among the n trials.

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 test statistic falls within the critical​ region, the decision is to reject the null hypothesis. C.If ​P-value ≤ α​, the decision is to reject the null hypothesis.​ Otherwise, we fail to reject the null hypothesis. D.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.-this one

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

A.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. This is the correct answer. B.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. C.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. D.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 characteristic of the t​ test?

A.The Student t distribution has the same general bell shape as the standard normal distribution. B.The Student t distribution is different for different sample sizes. C.The Student t distribution has a mean of tequals=0 and a standard deviation of sequals=1. This is the correct answer. D.The t test is robust against a departure from normality.

Which of the following is NOT true when testing a claim about a standard deviation or​ variance?

A.The condition of a normally distributed population is a much stricter requirement for the chi squaredχ2 test than for the t test or the z test. B.The table for finding​ P-values does not usually give exact​ P-values as it only includes select values of alphaα and selected numbers of degrees of freedom. C.The​ P-value method and the classical method are not equivalent to the confidence interval method in that they may yield different results. This is the correct answer. D.The χ2 test is not robust against a departure from normality.

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 sample observations are a simple random sample. B.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.Your answer is correct. C.The conditions for a binomial distribution are satisfied. D.The conditions np>5 and nq >5 are both satisfied.

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

A.The​ P-value is an area. B.If the P is​ high, the null will fly. C.If the P is​ low, the null must go. D.The​ P-value separates the critical region from the values that do not lead to rejection of 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 equals n minus 1.df=n− 1. B.The values of​ chi-square can be zero or​ positive, but they cannot be negative. C. The​ chi-square distribution is not symmetric. D. The mean of the​ chi-square distribution is 0.- this one

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

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

Type 1 error

Rejecting null hypothesis when it is true

Which of the following is NOT a requirement for testing a claim about a standard deviation or​ variance?

The population must be skewed to the right.

p value

The probability of observing a test statistic as extreme as, or more extreme than, the statistic obtained from a sample, under the assumption that the null hypothesis is true.

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

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

Which of the following is not a strategy for finding​ P-values with the Student t​ distribution?

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