Deck 10: Introduction to Hypothesis Testing

Question 1

In testing a hypothesis, statements for the null and alternative hypotheses as well as the selection of the level of significance should precede the collection and examination of the data.

Answer 1

True

Question 2

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

Answer 2

False

Question 3

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

Answer 3

False

Question 4

A Type II error is represented by a ; it is the probability of rejecting a true null hypothesis.

Question 5

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.

Question 6

An alternative or research hypothesis is an assertion that holds if the null hypothesis is false.

Question 7

A p -value is usually set at 0.05.

Question 8

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

Question 9

A Type I error is represented by b .

Question 10

A Type II error is represented by b ; it is the probability of failing to reject a false null hypothesis.

Question 11

Increasing the probability of a Type I error will increase the probability of a Type II error.

Question 12

In a criminal trial, a Type I error is made when an innocent person is convicted.

Question 13

Reducing the probability of a Type I error also reduces the probability of a Type II error.

Question 14

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

Question 15

A Type I error is represented by a ; it is the probability of rejecting a true null hypothesis.

Question 16

The statement of the null hypothesis always includes an equals sign (=).

Question 17

In a criminal trial, a Type II error is made when an innocent person is acquitted.

Question 18

A null hypothesis is a statement about the value of a population parameter.

Question 19

There is an inverse relationship between the probabilities of Type I and Type II errors; as one increases, the other decreases, and vice versa.

Question 20

It is possible to commit a Type I error and a Type II error at the same time.

Question 21

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

Question 22

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

Question 23

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

Question 24

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

Question 25

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.

Question 26

A sample is used to obtain a 95% confidence interval for the mean of a population. The confidence interval goes from 10.89 to 13.21. If the same sample had been used to test H ₀: m = 12 vs. H ₁: m ¹ 12, H ₀ could not be rejected at the 0.05 level.

Question 27

If your p -value is greater than 0.900 you should reject H ₀ at the 0.10 level.

Question 28

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

Question 29

A two-tail test for the population mean m produces a test-statistic z = 1.89. The p -value associated with the test is 0.0588.

Question 30

There is a direct relationship between the power of a test and the probability of a Type II error.

Question 31

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

Question 32

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

Question 33

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

Question 34

A one-tail test for the population mean m produces a test-statistic z = - 0.75. The p -value associated with the test is 0.7734.

Question 35

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

Question 36

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

Question 37

The power of the test refers to the probability of rejecting a false null hypothesis.

Question 38

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

Question 39

For a given level of significance, if the sample size is increased, the power of the test will increase.

Question 40

If a sample size is increased at a given a level, the probability of committing a Type II error is increased.

Question 41

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

Question 42

One way of expressing how well a test performs is to report its power --the probability of detecting a false null hypothesis.

Question 43

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.

Question 44

The operating characteristic curve plots the values of b (the probability of committing a Type II error)versus the values of the population mean m .

Question 45

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.

Question 46

For a given sample size, the probability of committing a Type II error will increase when the probability of committing a Type I error is reduced.

Question 47

We cannot commit a Type I error when the:

A)null hypothesis is true.
B)level of significance is 0.10.
C)null hypothesis is false.
D)test is a two-tail test.

Question 48

The probability of a Type I error is denoted by:

A)b
B)1 - b
C)a
D)1 - a

Question 49

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:

A)H ₀: m = 1200 vs. H ₁: m 1200
B)H ₀: m > 1200 vs. H ₁: m = 1200
C)H ₀: m = 1200 vs. H ₁: m > 1200
D)H ₀: m 1200 vs. H ₁: m = 1200

Question 50

In a criminal trial, a Type I error is made when:

A)a guilty defendant is acquitted.
B)an innocent person is convicted.
C)a guilty defendant is convicted.
D)an innocent person is acquitted.

Question 51

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.

Question 52

In a criminal trial, a Type II error is made when:

A)a guilty defendant is acquitted.
B)an innocent person is convicted.
C)a guilty defendant is convicted.
D)an innocent person is acquitted.

Question 53

A Type I error occurs when we:

A)reject a false null hypothesis.
B)reject a true null hypothesis.
C)don't reject a false null hypothesis.
D)don't reject a true null hypothesis.

Question 54

Which of the following conclusions is not an appropriate conclusion from a hypothesis test?

A)Reject H ₀. Sufficient evidence to support H ₁.
B)Fail to reject H ₀. Insufficient evidence to support H ₁.
C)Accept H ₀. Sufficient evidence to support H ₀.
D)All of these choices are true.

Question 55

The power of a test is the probability that a true null hypothesis will be rejected.

Question 56

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)H ₀: m ¹ 3 vs. H ₁: m > 3
B)H ₀: m = 3 vs. H ₁: m ¹ 3
C)H ₀: m ¹ 3 vs. H ₁: m = 3
D)H ₀: m = 3 vs. H ₁: m 3

Question 57

The probability of a Type II error is denoted by:

A)a
B)b
C)1 - a
D)1 - b

Question 58

A Type II error is defined as:

A)rejecting a true null hypothesis.
B)rejecting a false null hypothesis.
C)not rejecting a true null hypothesis.
D)not rejecting a false null hypothesis.

Question 59

As the alternative value of m increases, so does the power of the test.

Question 60

The hypothesis of most interest to the researcher is:

A)the alternative hypothesis.
B)the null hypothesis.
C)both hypotheses are of equal interest.
D)Neither hypothesis is of interest.

Question 61

Suppose we wish to test H ₀: m = 45 vs. H ₁: m > 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.

Question 62

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)H ₀: m = 40 vs. H ₁: m > 40
B)H ₀: m = 40 vs. H ₁: m 40
C)H ₀: = 40 vs. H ₁: 40
D)H ₀: m 40 vs. H ₁: m = 40

Question 63

In testing the hypotheses H ₀: m = 50 vs. H ₁: m ¹ 50, the following information is known: n = 64, = 53.5, and s = 10. The standardized test statistic z equals:

A)1.96
B)- 2.80
C)2.80
D)- 1.96

Question 64

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.

Question 65

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.

Question 66

Suppose that we reject a null hypothesis at the 0.05 level of significance. Then for which of the following a -values do we also reject the null hypothesis?

A)0.06
B)0.04
C)0.03
D)0.02

Question 67

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.

Question 68

In testing the hypotheses H ₀: m = 800 vs. H ₁: m ¹ 800, 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

Question 69

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.

Question 70

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.

Question 71

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.

Question 72

If we reject the null hypothesis when it is false, then we have committed:

A)a Type II error.
B)a Type I error.
C)both a Type I error and a Type II error.
D)neither a Type I error nor a Type II error.

Question 73

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.

Question 74

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.

Question 75

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:

A)H ₀: m = 30 vs. H ₁: m 30.
B)H ₀: m = 30 vs. H ₁: m > 30.
C)H ₀: = 30 vs. H ₁: 30.
D)H ₀: = 30 vs. H ₁: > 30.

Question 76

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

Question 77

In testing the hypotheses H ₀: m = 75 vs. H ₁: m z equals - 2.42, then the p -value is:

A)0.5078
B)2.4200
C)0.9922
D)0.0078

Question 78

Which of the following probabilities is equal to the significance level a ?

A)Probability of making a Type I error.
B)Probability of making a Type II error.
C)Probability of rejecting H ₀ when you are supposed to.
D)Probability of not rejecting H ₀ when you shouldn't.

Question 79

The critical values z _a or z _{a \ 2} are the boundary values for:

A)the rejection region(s).
B)the level of significance.
C)Type I error.
D)Type II error.

Question 80

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