ECO6415 Ch 11

If your p-value is greater than 0.900 you should reject H0 at the 0.10 level.

false

A sample is used to obtain a 95% confidence interval for the mean of a population. The confidence interval goes from 78.21 to 87.64. If the same sample had been used to test the null hypothesis that the mean of the population differs from 90, the null hypothesis could be rejected at a level of significance of 0.05.

true

For a given level of significance, if the sample size is increased, the probability of committing a Type II error will decrease

true

If we reject a null hypothesis at the 0.05 level of significance, then we must also reject it at the 0.10 level.

true

In testing the hypotheses H0: 50 vs. H1: 50, the following information is known: n = 64, = 53.5, and = 10. The standardized test statistic z equals:

2.80

In testing the hypotheses H0: 800 vs. H1: 800, if the value of the test statistic equals 1.75, then the p-value is: a. 0.0401 b. 0.0802 c. 0.4599 d. 0.9599

b. 0.0802

Suppose that we reject a null hypothesis at the 0.05 level of significance. Then for which of the following -values do we also reject the null hypothesis? a. 0.06 b. 0.04 c. 0.03 d. 0.02

a. 0.06

A professor of linguistics refutes the claim that the average student spends 3 hours studying for the midterm exam. She thinks they spend more time than that. Which hypotheses are used to test the claim?

a. H0: u= 3 vs. H1: u > 3

A one-tail p-value is two times the size of a two-tail test.

false

In a one-tail test, the p-value is found to be equal to 0.054. If the test had been two-tail, then the p-value would have been 0.027.

false

In order to determine the p-value, it is necessary to know the level of significance

false

The larger the p-value, the more likely one is to reject the null hypothesis.

false

The p-value is the probability that the null hypothesis is true.

false

The owner of a local Jazz Club has recently surveyed a random sample of n = 200 customers of the club. She would now like to determine whether or not the mean age of her customers is over 30. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. The appropriate hypotheses to test are

B. b. H0: u= 30 vs. H1: u> 30.

Which of the following probabilities is equal to the significance level ? a. Probability of making a Type I error. b. Probability of making a Type II error. c. Probability of rejecting H0 when you are supposed to. d. Probability of not rejecting H0 when you shouldn't.

a. Probability of making a Type I error.

We have created a 95% confidence interval for with the result (8, 13). What conclusion will we make if we test H0: 15 vs. H1: 15 at = 0.05? a. Reject H0 in favor of H1 b. Accept H0 in favor of H1 c. Fail to reject H0 in favor of H1 d. We cannot tell what our decision will be from the information given

a. Reject H0 in favor of H1

In order to determine the p-value, which of the following is not needed? a. The level of significance. b. Whether the test is one-tail or two-tail. c. The value of the test statistic. d. All of these choices are true.

a. The level of significance

Which of the following is an appropriate null hypothesis? a. The mean of a population is equal to 60. b. The mean of a sample is equal to 60. c. The mean of a population is not equal to 60. d. All of these choices are true.

a. The mean of a population is equal to 60.

In testing the hypothesis H0: 100 vs. H1: > 100, the p-value is found to be 0.074, and the sample mean is 105. Which of the following statements is true? a. The probability of observing a sample mean at least as large as 105 from a population whose mean is 100 is 0.074. b. The probability of observing a sample mean smaller than 105 from a population whose mean is 100 is 0.074. c. The probability that the population mean is larger than 100 is 0.074. d. None of these choices.

a. The probability of observing a sample mean at least as large as 105 from a population whose mean is 100 is 0.074.

In a criminal trial, a Type II error is made when: a. a guilty defendant is acquitted. c. a guilty defendant is convicted. b. an innocent person is convicted. d. an innocent person is acquitted.

a. a guilty defendant is acquitted.

The p-value of a test is the: a. smallest at which the null hypothesis can be rejected. b. largest at which the null hypothesis can be rejected. c. smallest at which the null hypothesis cannot be rejected. d. largest at which the null hypothesis cannot be rejected.

a. smallest at which the null hypothesis can be rejected.

The hypothesis of most interest to the researcher is: a. the alternative hypothesis. c. both hypotheses are of equal interest. b. the null hypothesis. d. Neither hypothesis is of interest.

a. the alternative hypothesis.

If we reject the null hypothesis, we conclude that: a. there is enough statistical evidence to infer that the alternative hypothesis is true. b. there is not enough statistical evidence to infer that the alternative hypothesis is true. c. there is enough statistical evidence to infer that the null hypothesis is true. d. there is not enough statistical evidence to infer that the null hypothesis is true.

a. there is enough statistical evidence to infer that the alternative hypothesis is true

The probability of a Type I error is denoted by: a. c. b. 1 d. 1

alpha

Researchers claim that 40 tissues is the average number of tissues a person uses during the course of a cold. The company who makes Puffs brand tissues thinks that fewer of their tissues are needed. What are their null and alternative hypotheses? a. H0: 40 vs. H1: 40 c. H0: 40 vs. H1: 40 b. H0: 40 vs. H1: 40 d. H0: 40 vs. H1: 40

b. H0: u= 40 vs. H1: u<40

Which of the following statements is not true? a. The probability of making a Type II error increases as the probability of making a Type I error decreases. b. The probability of making a Type II error and the level of significance are the same. c. The power of the test decreases as the level of significance decreases. d. All of these choices are true.

b. The probability of making a Type II error and the level of significance are the same

In a criminal trial, a Type I error is made when: a. a guilty defendant is acquitted. c. a guilty defendant is convicted. b. an innocent person is convicted. d. an innocent person is acquitted.

b. an innocent person is convicted

If a test of hypothesis has a Type I error probability of .05, this means that: a. if the null hypothesis is true, we don't reject if 5% of the time. b. if the null hypothesis is true, we reject it 5% of the time. c. if the null hypothesis is false, we don't reject it 5% of the time. d. if the null hypothesis is false, we reject it 5% of the time.

b. if the null hypothesis is true, we reject it 5% of the time.

If a hypothesis is rejected at the 0.025 level of significance, it: a. must be rejected at any level. b. must be rejected at the 0.01 level. c. must not be rejected at the 0.01 level. d. may or may not be rejected at the 0.01 level.

b. must be rejected at the 0.01 level.

The p-value criterion for hypothesis testing is to reject the null hypothesis if: a. p-value = b. p-value < c. p-value > d. < p-value <

b. p-value <

A Type I error occurs when we: a. reject a false null hypothesis. c. don't reject a false null hypothesis. b. reject a true null hypothesis. d. don't reject a true null hypothesis.

b. reject a true null hypothesis

If the p value is less than in a two-tail test: a. the null hypothesis should not be rejected. b. the null hypothesis should be rejected. c. a one-tail test should be used. d. No conclusion should be reached.

b. the null hypothesis should be rejected.

47. If we do not reject the null hypothesis, we conclude that: a. there is enough statistical evidence to infer that the alternative hypothesis is true. b. there is not enough statistical evidence to infer that the alternative hypothesis is true. c. there is enough statistical evidence to infer that the null hypothesis is true. d. there is not enough statistical evidence to infer that the null hypothesis is true.

b. there is not enough statistical evidence to infer that the alternative hypothesis is true.

The rejection region for testing H0: 100 vs. H1: 100, at the 0.05 level of significance is: a. | z | < 0.95 b. | z | > 1.96 c. z > 1.65 d. z < 2.33

b. | z | > 1.96

The probability of a Type II error is denoted by:

beta

. Suppose that in a certain hypothesis test the null hypothesis is rejected at the .10 level; it is also rejected at the .05 level; however it cannot be rejected at the .01 level. The most accurate statement that can be made about the p-value for this test is that: a. p-value = 0.01. b. p-value = 0.10. c. 0.01 < p-value < 0.05. d. 0.05 < p-value < 0.10.

c. 0.01 < p-value < 0.05.

The owner of a local nightclub has recently surveyed a random sample of n = 300 customers of the club. She would now like to determine whether or not the mean age of her customers is over 35. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. Suppose she found that the sample mean was 35.5 years and the population standard deviation was 5 years. What is the p-value associated with the test statistic? a. 0.9582 b. 1.7300 c. 0.0418 d. 0.0836

c. 0.0418

Which of the following conclusions is not an appropriate conclusion from a hypothesis test? a. Reject H0. Sufficient evidence to support H1. b. Fail to reject H0. Insufficient evidence to support H1. c. Accept H0. Sufficient evidence to support H0. d. All of these choices are true.

c. Accept H0. Sufficient evidence to support H0.

A spouse suspects that the average amount of money spent on Christmas gifts for immediate family members is above $1,200. The correct set of hypotheses is:

c. H0: u = 1200 vs. H1: u> 1200

The owner of a local Karaoke Bar has recently surveyed a random sample of n = 300 customers of the bar. She would now like to determine whether or not the mean age of her customers is over 35. If so, she plans to alter the entertainment to appeal to an older crowd. If not, no entertainment changes will be made. If she wants to be 99% confident in her decision, what rejection region she use if the population standard deviation is known? a. Reject H0 if z < 2.33 b. Reject H0 if z < 2.58 c. Reject H0 if z > 2.33 d. Reject H0 if z > 2.58

c. Reject H0 if z > 2.33

A Type II error is committed if we make: a. a correct decision when the null hypothesis is false. b. a correct decision when the null hypothesis is true. c. an incorrect decision when the null hypothesis is false. d. an incorrect decision when the null hypothesis is true.

c. an incorrect decision when the null hypothesis is false

Using a confidence interval when conducting a two-tail test for , we do not reject H0 if the hypothesized value for : a. is to the left of the lower confidence limit (LCL). b. is to the right of the upper confidence limit (UCL). c. falls between the LCL and UCL. d. falls in the rejection region.

c. falls between the LCL and UCL.

We cannot commit a Type I error when the: a. null hypothesis is true. c. null hypothesis is false. b. level of significance is 0.10. d. test is a two-tail test.

c. null hypothesis is false

61. The numerical quantity computed from the data that is used in deciding whether to reject H0 is the: a. significance level. b. critical value. c. test statistic. d. parameter.

c. test statistic.

If a hypothesis is not rejected at the 0.10 level of significance, it: a. must be rejected at the 0.05 level. b. may be rejected at the 0.05 level. c. will not be rejected at the 0.05 level. d. must be rejected at the 0.025 level.

c. will not be rejected at the 0.05 level.

If a null hypothesis is rejected at the 0.05 level of significance, it must be rejected at the 0.025 level

false

In a two-tail test for the population mean, if the null hypothesis is rejected when the alternative hypothesis is true: a. a Type I error is committed. b. a Type II error is committed. c. a correct decision is made. d. a one-tail test should be used instead of a two-tail test.

c. a correct decision is made.

For a two-tail test, the null hypothesis will be rejected at the 0.05 level of significance if the value of the standardized test statistic z is: a. smaller than 1.96 or greater than 1.96 b. greater than 1.96 or smaller than 1.96 c. smaller than 1.96 or greater than 1.96 d. greater than 1.645 or less than 1.645

c.. smaller than 1.96 or greater than 1.96

Which of the following would be an appropriate alternative hypothesis? a. The mean of a population is equal to 70. b. The mean of a sample is equal to 70. c. The mean of a population is greater than 70. d. The mean of a sample is greater than 70.

c.The mean of a population is greater than 70.

In testing the hypotheses H0: 75 vs. H1: < 75, if the value of the test statistic z equals 2.42, then the p-value is: a. 0.5078 b. 2.4200 c. 0.9922 d. 0.0078

d. 0.0078

Which of the following p-values will lead us to reject the null hypothesis if the level of significance equals 0.05? a. 0.150 b. 0.100 c. 0.051 d. 0.025

d. 0.025

In a one-tail test, the p-value is found to be equal to 0.068. If the test had been two-tail, the p-value would have been: a. 0.932 b. 0.466 c. 0.034 d. 0.136

d. 0.136

Statisticians can translate p-values into several descriptive terms. Suppose you typically reject H0 at level 0.05. Which of the following statements is correct? a. If the p-value < 0.001, there is overwhelming evidence to infer that the alternative hypothesis is true. b. If 0.01 < p-value < 0.05, there is evidence to infer that the alternative hypothesis is true. c. If p-value > 0.10, there is no evidence to infer that the alternative hypothesis is true. d. All of these choices are true.

d. All of these choices are true.

The level of significance can be: a. any number between 1.0 and 1.0. b. any number greater than zero. c. any number greater than 1.96 or less than 1.96. d. None of these choices.

d. None of these choices.

We have created a 95% confidence interval for with the results (10, 25). What conclusion will we make if we test H0: 26 vs. H1: 26 at = 0.025? a. Reject H0 in favor of H1 b. Accept H0 in favor of H1 c. Fail to reject H0 in favor of H1 d. We cannot tell from the information given.

d. We cannot tell from the information given

Suppose we wish to test H0: vs. H1: 45. What will result if we conclude that the mean is greater than 45 when the actual mean is 50? a. We have made a Type I error. b. We have made a Type II error. c. We have made both a Type I error and a Type II error. d. We have made the correct decision.

d. We have made the correct decision

A Type I error is committed if we make: a. a correct decision when the null hypothesis is false. b. a correct decision when the null hypothesis is true. c. an incorrect decision when the null hypothesis is false. d. an incorrect decision when the null hypothesis is true.

d. an incorrect decision when the null hypothesis is true.

If we reject the null hypothesis when it is false, then we have committed: a. a Type II error. c. both a Type I error and a Type II error. b. a Type I error. d. neither a Type I error nor a Type II error.

d. neither a Type I error nor a Type II error.

A Type II error is defined as: a. rejecting a true null hypothesis. c. not rejecting a true null hypothesis. b. rejecting a false null hypothesis. d. not rejecting a false null hypothesis.

d. not rejecting a false null hypothesis.

49. If the value of the sample mean is close enough to the hypothesized value 0 of the population mean , then: a. the value of 0 is definitely correct. b. the value of 0 is definitely wrong. c. we reject the null hypothesis. d. we cannot reject the null hypothesis.

d. we cannot reject the null hypothesis.

The rejection region for testing H0: 80 vs. H1: 80, at the 0.10 level of significance is: a. z > 1.96 b. z < 0.90 c. z > 1.28 d. z < 1.28

d. z < 1.28

In a two-tail test for the population mean, the null hypothesis will be rejected at level of significance if the value of the standardized test statistic z is such that: a. z > z b. z < z c. z < z < z d. | z | > z / 2

d. | z | > z / 2

If we do not reject the null hypothesis, we conclude that there is enough statistical evidence to infer that the null hypothesis is true.

false

A p-value is usually set at 0.05

false

For a given level of significance, if the sample size is increased, the probability of committing a Type I error will decrease.

false

If we reject the null hypothesis, we conclude that there is enough statistical evidence to infer that the alternative hypothesis is true.

true

The critical values will bound the rejection and non-rejection regions for the null hypothesis.

true

The p-value of a test is the probability of observing a test statistic at least as extreme as the one computed given that the null hypothesis is true.

true

The p-value of a test is the smallest at which the null hypothesis can be rejected.

true

Using the confidence interval when conducting a two-tail test for the population mean , we do not reject the null hypothesis if the hypothesized value for falls between the lower and upper confidence limits.

true

p-value is a probability, and must be between 0 and 1

true