Deck 11: Introduction to Hypothesis Testing

Question 1

A Type I error is represented by $\beta$ .

Answer 1

False

Question 2

The probability of a Type I error is denoted by:

A) $\beta$
B) 1- $\beta$
C) $\alpha$
D) 1 - $\alpha$

Answer 2

$\alpha$

Question 3

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

Answer 3

False

Question 4

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

Question 5

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 6

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

Question 7

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

Question 8

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.

Question 9

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

Question 10

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

Question 11

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: $\mu$ =3 vs.H₁: $\mu$ >3
B) H₀: $\mu$ = 3 vs.H₁: $\mu$$\neq$ 3
C) H₀: $\mu$ $\neq$ 3 vs.H₁: $\mu$ = 3
D) H₀: $\mu$ =3 vs.H₁: $\mu$ <3

Question 12

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

Question 13

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

Question 14

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

Question 15

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 16

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 17

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 18

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

Question 19

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

Question 20

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

Question 21

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 22

If a researcher fails to reject a false null hypothesis he has made a(n) ____________________ error.

Question 23

Suppose we wish to test H₀: $\mu$ =45vs.H₁: $\mu$ > 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 24

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: $\mu$ =40 vs.H₁: $\mu$ >40
B) H₀: $\mu$ =40 vs.H₁:<40
C) H₀:= 40 vs.H₁:< 40
D) H₀: $\mu$ <40 vs.H₁: $\mu$ =40

Question 25

If a researcher rejects a true null hypothesis, she has made a(n) ____________________ error.

Question 26

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 27

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 28

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 29

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) H₀: $\mu$ = 1200 vs.H₁: $\mu$ <1200
B) H₀: $\mu$ >1200 vs.H₁: $\mu$ =1200
C) H₀: $\mu$ =1200 vs.H₁: $\mu$ >1200
D) H₀: $\mu$ <1200 vs.H₁: $\mu$ =1200

Question 30

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 31

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 32

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 33

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.

Question 34

The probability of a Type II error is denoted by:

A) $\alpha$
B) $\beta$
C) 1 - $\alpha$
D) 1- $\beta$

Question 35

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) H₀: $\mu$ =30 vs.H₁: $\mu$ <30.
B) H₀: $\mu$ =30 vs.H₁: $\mu$ <30.
C) H₀:= 30 vs.H₁:< 30.
D) H₀:= 30 vs.H₁:> 30.

Question 36

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 37

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 38

Which of the following probabilities is equal to the significance level $\alpha$ ?

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.

Question 39

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 40

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 41

A p-value is usually set at 0.05.

Question 42

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

Question 43

Think about a situation where you have a test for a virus.First, you are tested positive or negative.Second, you either really do have the virus or you don't.
a.
If you actually have the virus but the test did not catch it, which error has been made and what is the impact of that error?
b.
If you actually don't have the virus but the test says you did, which error is being made and what is the impact of this error?
c.
Which error is the worst one to commit in this situation and why?

Question 44

After you set up the hypotheses and collect your data, you calculate the statistic that serves as the criterion for making your decision.This number is called the ____________________ statistic.

Question 45

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 46

If a researcher rejects a false null hypothesis, she has made a(n) ____________________ decision.

Question 47

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

Question 48

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 49

Suppose a pickup and delivery company states that their packages arrive within two days or less on average.You want to find out whether the actual average delivery time is longer than this.You conduct a hypothesis test.
a.
Set up the null and alternative hypotheses.
b.
Suppose you conclude wrongly that the company's statement about average delivery time is within two days.What type of error is being committed and what is the impact of that error?
c.
Suppose you conclude wrongly that the delivery company's average time to delivery is in fact longer than two days.What type of error did you commit and what is the impact of this error?
d.
Which error is worse from the company's standpoint, a Type I or a Type II error? Why?
e.
Which error is worse from a consumer standpoint, a Type I or a Type II error? Why?

Question 50

You cannot commit a(n) ____________________ error when the null hypothesis is false.

Question 51

The probability of a Type II error is denoted by ____________________.

Question 52

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

Question 53

You cannot commit a(n) ____________________ error when the null hypothesis is true.

Question 54

Suppose an auto manufacturer states that their car goes from 0 to 60 miles per hour in 10 seconds on average, and you suspect that time is longer.
a.
Set up the null and alternative hypotheses to test this claim.
b.
Explain how you know which is the null hypothesis and which is the alternative hypothesis.

Question 55

Explain the difference between accepting H₀ and failing to reject H₀.

Question 56

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

Question 57

Explain why a Type I error and a Type II error have an inverse relationship.

Question 58

If a researcher fails to reject a true null hypothesis, he has made a(n) ____________________ decision.

Question 59

The probability of a Type I error is denoted by ____________________.

Question 60

The hypothesis testing procedure begins with the assumption that the null hypothesis is ____________________.

Question 61

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 62

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

Question 63

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

Question 64

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

Question 65

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

Question 66

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

Question 67

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

Question 68

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

Question 69

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 70

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

Question 71

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

Question 72

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.

Question 73

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 H₀: $\mu$ = 12 vs.H₁: $\mu$ $\neq$ 12, H₀ could not be rejected at the 0.05 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

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

Question 76

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

Question 77

In testing the hypotheses H₀: $\mu$ = 75 vs.H₁: $\mu$ < 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

Question 78

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

Question 79

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 80

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