Deck 9: Hypothesis Testing

Question 1

The hypothesis statement H: < 60 is an example of a(an)________ hypothesis.

Answer 1

alternative

Question 2

The critical value approach specifies a region of values,also called the ________ region.

Answer 2

rejection

Question 3

The _______ value approach specifies a region of values such that if the value of the test statistic falls into this region,then we reject the null hypothesis.

Answer 3

critical

Question 4

A(n)______ error is committed when we reject the null hypothesis when the null hypothesis is true.

Question 5

We define the allowed probability of making a Type I error as α,and we refer to 100α% as the ____________.

Question 6

Given the _________ of the z distribution,the p-value for a two-tailed test is twice that of the p-value for a one-tailed test.

Question 7

The null hypothesis typically corresponds to a presumed default state of nature.

Question 8

If we reject a null hypothesis at the 1% significance level,then we have _________ evidence that the null hypothesis is false.

Question 9

Under the assumption that the null hypothesis is true as an equality,the p-value is the likelihood of observing a sample mean that is at least as extreme as the one derived from the given sample.

Question 10

Excel's function _______ returns the p-value for a right-tailed test.

Question 11

The critical value approach specifies a range of values,also called the rejection region,such that if the value of the test statistic falls into this range,we do not reject the null hypothesis.

Question 12

The hypothesis statement H: µ = 25 is an example of a(an)________ hypothesis.

Question 13

A hypothesis test regarding the population mean µ is based on the sampling distribution of the sample mean

Question 14

In a one-tailed test,the rejection region is located under one tail (left or right)of the corresponding probability distribution,while in a two-tailed test this region is located under both tails.

Question 15

A Type II error is made when we reject the null hypothesis and the null hypothesis is actually false.

Question 16

The alternative hypothesis typically agrees with the status quo.

Question 17

For a given sample size,any attempt to reduce the likelihood of making one type of error (Type I or Type II)will increase the likelihood of the other error.

Question 18

As a general guideline,we use the alternative hypothesis as a vehicle to establish something new,or contest the status quo,for which a corrective action may be required.

Question 19

A Type I error is committed when we reject the null hypothesis,which is actually true.

Question 20

On the basis of sample information,we either "accept the null hypothesis" or "reject the null hypothesis."

Question 21

A Type I error occurs when we ___________.

A) reject the null hypothesis when it is actually true
B) reject the null hypothesis when it is actually false
C) do not reject the null hypothesis when it is actually true
D) do not reject the null hypothesis when it is actually false

Question 22

A statistics professor works tirelessly to catch students cheating on his exams.He has particular routes for his teaching assistants to patrol,an elevated chair to ensure an unobstructed view of all students,and even a video recording of the exam in case additional evidence needs to be collected.He estimates that he catches 95% of students who cheat in his class,but 1% of the time that he accuses a student of cheating he is actually incorrect.Consider the null hypothesis,"the student is not cheating." What is the probability of a Type I error?

A) 1%
B) 5%
C) 95%
D) 99%

Question 23

For a given sample size n,_______________________________________________________________.

A) decreasing the probability of a Type I error α will increase the probability of a Type II error β
B) decreasing the probability of a Type I error α will decrease the probability of a Type II error β
C) changing the probability of a Type I error α will have no impact on the probability of a Type II error β
D) increasing the probability of a Type I error α will increase the probability of a Type II error β as long as σ is known

Question 24

The alternative hypothesis typically ___________.

A) corresponds to the presumed default state of nature
B) contests the status quo,for which a corrective action may be required
C) states the probability of rejecting the null hypothesis when it is false
D) states the probability of rejecting the null hypothesis when it is true

Question 25

It is generally believed that no more than 0.50 of all babies in a town in Texas are born out of wedlock.A politician claims that the proportion of babies born out of wedlock is increasing.Identify the correct null and alternative hypotheses to test the politician's claim.

A) H₀:p = 0.50 and H_A:p ≠ 0.50
B) H₀:p ≤ 0.50 and H_A:p > 0.50
C) H₀:p ≥ 0.50 and H_A:p > 0.50
D) H₀:p ≥ 0.50 and H_A:p < 0.50

Question 26

A fast-food franchise is considering building a restaurant at a busy intersection.A financial advisor determines that the site is acceptable only if,on average,more than 300 automobiles pass the location per hour.The advisor tests the following hypotheses: H_o: μ ≤ 300.
H_A: μ > 300.
The consequences of committing a Type I error would be that____________________________.

A) the franchiser builds on an acceptable site
B) the franchiser builds on an unacceptable site
C) the franchiser does not build on an acceptable site
D) the franchiser does not build on an unacceptable site

Question 27

A Type II error occurs when we ___________.

A) reject the null hypothesis when it is actually true
B) reject the null hypothesis when it is actually false
C) do not reject the null hypothesis when it is actually true
D) do not reject the null hypothesis when it is actually false

Question 28

It is generally believed that no more than 0.50 of all babies in a town in Texas are born out of wedlock.A politician claims that the proportion of babies born out of wedlock is increasing.In testing the politician's claim,how does one define the population parameter of interest?

A) The current proportion of babies born out of wedlock
B) The mean number of babies born out of wedlock
C) The number of babies born out of wedlock
D) The general belief that the proportion of babies born out of wedlock is no more than 0.50

Question 29

A local courier service advertises that its average delivery time is less than 6 hours for local deliveries.When testing the two hypotheses,H_o:μ ≥ 6 and H_A:μ < 6,μ stand for _____________.

A) the mean delivery time
B) the standard deviation of the delivery time
C) the number of deliveries that took less than 6 hours
D) the proportion of deliveries that took less than 6 hours

Question 30

Many cities around the United States are installing LED streetlights,in part to combat crime by improving visibility after dusk.An urban police department claims that the proportion of crimes committed after dusk will fall below the current level of 0.84 if LED streetlights are installed.Specify the null and alternative hypotheses to test the police department's claim.

A) H₀:p = 0.84 and H_A:p ≠ 0.84
B) H₀:p < 0.84 and H_A:p ≥ 0.84
C) H₀:p ≤ 0.84 and H_A:p > 0.84
D) H₀:p ≥ 0.84 and H_A:p < 0.84

Question 31

Consider the following hypotheses that relate to the medical field: H_o: A person is free of disease.
H_A: A person has disease.
In this instance,a Type I error is often referred to as ___________.

A) a false positive
B) a false negative
C) a negative result
D) the power of the test

Question 32

Consider the following hypotheses that relate to the medical field: H_o: A person is free of disease.
H_A: A person has disease.
In this instance,a Type II error is often referred to as ___________.

A) a false positive
B) a false negative
C) a negative result
D) the power of the test

Question 33

When we reject the null hypothesis when it is actually false,we have committed _________.

A) no error
B) a Type I error
C) a Type II error
D) a Type I error and a Type II error

Question 34

To obtain the p-value for a right-tailed test of the population mean,when σ is unknown,we use the Excel's function _________.

Question 35

A professional sports organization is going to implement a test for steroids.The test gives a positive reaction in 94% of the people who have taken the steroid.However,it erroneously gives a positive reaction in 4% of the people who have not taken the steroid.What is the probability of Type I and Type II errors giving the null hypothesis "the individual has not taken steroids."

A) Type I: 4%,Type II: 6%
B) Type I: 6%,Type II: 4%
C) Type I: 94%,Type II: 4%
D) Type I: 4%,Type II: 94%

Question 36

The null hypothesis in a hypothesis test refers to _____________.

A) the desired outcome
B) the default state of nature
C) the altered state of nature
D) the desired state of nature

Question 37

It is generally believed that no more than 0.50 of all babies in a town in Texas are born out of wedlock.A politician claims that the proportion of babies born out of wedlock is increasing.When testing the two hypotheses,H₀: p ≤ 0.50 and H_A: p > 0.50,p stands for _____________.

A) the current proportion of babies born out of wedlock
B) the mean number of babies born out of wedlock
C) the number of babies born out of wedlock
D) the general belief that the proportion of babies born out of wedlock is no more than 0.50

Question 38

In general,the null and alternative hypotheses are __________.

A) additive
B) correlated
C) multiplicative
D) mutually exclusive

Question 39

Which of the following types of tests may be performed?

A) Right-tailed and two-tailed tests
B) Left-tailed and two-tailed tests
C) Right-tailed and left-tailed tests
D) Right-tailed,left-tailed,and two-tailed tests

Question 40

The national average for an eighth-grade reading comprehension test is 73.A school district claims that its eighth-graders outperform the national average.In testing the school district's claim,how does one define the population parameter of interest?

A) The mean score on the eighth-grade reading comprehension test
B) The number of eighth graders who took the reading comprehension test
C) The standard deviation of the score on the eighth-grade reading comprehension test
D) The proportion of eighth graders who scored above 73 on the reading comprehension test

Question 41

A two-tailed hypothesis test of the population mean or population proportion has ________.

A) only one critical value
B) two critical values,both positive
C) two critical values,both negative
D) two critical values,one positive and one negative

Question 42

If the p-value for a hypothesis test is 0.027 and the chosen level of significance is α = 0.05,then the correct conclusion is to ________________.

A) reject the null hypothesis
B) not reject the null hypothesis
C) reject the null hypothesis if σ = 10
D) not reject the null hypothesis if σ = 10

Question 43

When conducting a hypothesis test for a given sample size,if a is increased from 0.05 to 0.10,then __________________.

A) the probability of incorrectly rejecting the null hypothesis increases
B) the probability of incorrectly failing to reject the null hypothesis decreases
C) the probability of Type II error decreases
D) All of the above

Question 44

When conducting a hypothesis test for a given sample size,if the probability of a Type I error decreases,then the ______________________________________.

A) probability of Type II error decreases
B) probability of incorrectly rejecting the null hypothesis increases
C) probability of incorrectly accepting the null hypothesis increases
D) probability of incorrectly accepting the null hypothesis decreases

Question 45

A one-tailed hypothesis test of the population mean has ______________.

A) only one critical value
B) two critical values,both positive
C) two critical values,both negative
D) two critical values,one positive and one negative

Question 46

A fast-food franchise is considering building a restaurant at a busy intersection.A financial advisor determines that the site is acceptable only if,on average,more than 300 automobiles pass the location per hour.If the advisor tests the hypotheses H_o: μ ≤ 300 versus H_A: μ > 300,μ stands for ____________.

A) the average number of automobiles that pass the intersection per hour
B) the number of automobiles that pass the intersection per hour
C) the proportion of automobiles that pass the intersection per hour
D) the standard deviation of the number of automobiles that pass the intersection per hour

Question 47

If the chosen significance level is α = 0.05,then ____________________________________________.

A) there is a 5% probability of rejecting a true null hypothesis
B) there is a 5% probability of accepting a true null hypothesis
C) there is a 5% probability of rejecting a false null hypothesis
D) there is a 5% probability of accepting a false null hypothesis

Question 48

When conducting a hypothesis test concerning the population proportion,the value of the test statistic is calculated as ____________.

A)
B)
C)
D)

Question 49

Which of the following represents an appropriate set of hypotheses?

A)
B)
C)
D)

Question 50

What is the decision rule when using the p-value approach to hypothesis testing?

A) Reject H_o if the p-value > α.
B) Reject H_o if the p-value < α.
C) Do not reject H_o if the p-value < 1 - α.
D) Do not reject H_o if the p-value > 1 - α.

Question 51

Which of the following are two-tailed tests?

A) H_o:μ ≤ 10,H_A:μ > 10
B) H_o:μ = 10,H_A:μ ≠ 10
C) H_o:μ ≥ 400,H_A:μ < 400
D) Both H_o:μ ≤ 10,H_A:μ > 10 and H_o:μ ≥ 400,H_A:μ < 400

Question 52

When conducting a hypothesis test,which of the following decisions represents an error?

A) Rejecting the null hypothesis when it is true.
B) Rejecting the null hypothesis when it is false.
C) Not rejecting the null hypothesis when it is true.
D) Rejecting the null hypothesis when it is false and not rejecting the null hypothesis when it is true.

Question 53

A fast-food franchise is considering building a restaurant at a busy intersection.A financial advisor determines that the site is acceptable only if,on average,more than 300 automobiles pass the location per hour.The advisor tests the following hypotheses: H_o: μ ≤ 300.
H_A: μ > 300.
The consequences of committing a Type II error would be that__________________________.

A) the franchiser builds on an acceptable site
B) the franchiser builds on an unacceptable site
C) the franchiser does not build on an acceptable site
D) the franchiser does not build on an unacceptable site

Question 54

Which of the following are one-tailed tests?

A) H_o:μ ≤ 10,H_A:μ > 10
B) H_o:μ = 10,H_A:μ ≠ 10
C) H_o:μ ≥ 400,H_A:μ < 400
D) Both H_o:μ ≤ 10,H_A:μ > 10 and H_o:μ ≥ 400,H_A:μ < 400

Question 55

When conducting a hypothesis test concerning the population mean,and the population standard deviation is unknown,the value of the test statistic is calculated as __________.

A)
B)
C)
D)

Question 56

Which of the following answers represents the objective of a hypothesis test?

A) Rejecting the null hypothesis when it is true.
B) Rejecting the null hypothesis when it is false.
C) Not rejecting the null hypothesis when it is true.
D) Rejecting the null hypothesis when it is false and not rejecting the null hypothesis when it is true.

Question 57

If the p-value for a hypothesis test is 0.07 and the chosen level of significance is α =0.05,then the correct conclusion is to ____________________.

A) reject the null hypothesis
B) not reject the null hypothesis
C) reject the null hypothesis if σ = 10
D) not reject the null hypothesis if σ = 10

Question 58

If the null hypothesis is rejected at a 1% significance level,then _____________.

A) the null hypothesis will be rejected at a 5% significance level
B) the alternative hypothesis will be rejected at a 5% significance level
C) the null hypothesis will not be rejected at a 5% significance level
D) the alternative hypothesis will not be rejected at a 5% significance level

Question 59

A hypothesis test regarding the population mean is based on ________________________________.

A) the sampling distribution of the sample mean
B) the sampling distribution of the sample variance
C) the sampling distribution of the sample proportion
D) the sampling distribution of the sample standard deviation

Question 60

When conducting a hypothesis test concerning the population mean,and the population standard deviation is known,the value of the test statistic is calculated as _________.

A)
B)
C)
D)

Question 61

A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50.A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60.The population standard deviation is assumed to equal 0.40.To establish whether the mean GPA exceeds 3.50,the appropriate hypotheses are ______________.

A)
B)
C)
D)

Question 62

Consider the following competing hypotheses: H_o:μ = 0,H_A:μ ≠ 0.The value of the test statistic is z = −1.38.If we choose a 5% significance level,then we ___________________________________________.

A) reject the null hypothesis and conclude that the population mean is significantly different from zero
B) reject the null hypothesis and conclude that the population mean is not significantly different from zero
C) do not reject the null hypothesis and conclude that the population mean is significantly different from zero
D) do not reject the null hypothesis and conclude that the population mean is not significantly different from zero

Question 63

The Boston public school district has had difficulty maintaining on-time bus service for its students ("A Year Later,School Buses Still Late," Boston Globe,October 5,2011).Suppose the district develops a new bus schedule to help combat chronic lateness on a particularly woeful route.Historically,the bus service on the route has been,on average,12 minutes late.After the schedule adjustment,the first 36 runs were an average of eight minutes late.As a result,the Boston public school district claimed that the schedule adjustment was an improvement-students were not as late.Assume a population standard deviation for bus arrival time of 12 minutes.At the 1% significance level,does the evidence support the Boston public schools' claim?

A) No,because the p-value is greater than α.
B) Yes,because thep-value is greater than α.
C) No,because the value of the test statistic is less than the critical value.
D) Yes,because the value of the test statistic is less than the critical value.

Question 64

The Boston public school district has had difficulty maintaining on-time bus service for its students ("A Year Later,School Buses Still Late," Boston Globe,October 5,2011).Suppose the district develops a new bus schedule to help combat chronic lateness on a particularly woeful route.Historically,the bus service on the route has been,on average,12 minutes late.After the schedule adjustment,the first 36 runs were an average of eight minutes late.As a result,the Boston public school district claimed that the schedule adjustment was an improvement-students were not as late.Assume a population standard deviation for bus arrival time of 12 minutes.The value of the test statistic is ____________.

A) t₃₅ = -2.00
B) z = -2.00
C) t₃₅ = -0.33
D) z = -0.33

Question 65

The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership.The dealership has historically had 800 customers per day.The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750.Assume that the population standard deviation is 350.At a 5% significance level,the critical value(s)is(are)___________.

A) 1.645
B) -1.645
C) -1.96 and 1.96
D) -2.030 and 2.030

Question 66

The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership.The dealership has historically had 800 customers per day.The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750.Assume that the population standard deviation is 350.At the 5% significance level,the decision is to ___________.

A) reject H_o;we can conclude that the mean number of customers visiting the dealership is significantly less than 800
B) reject H_o;we cannot conclude that the mean number of customers visiting the dealership is significantly less than 800
C) do not reject H_o;we can conclude that the mean number of customers visiting the dealership is significantly less than 800
D) do not reject H_o;we cannot conclude that the mean number of customers visiting the dealership is significantly less than 800

Question 67

The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership.The dealership has historically had 800 customers per day.The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750.Assume that the population standard deviation is 350.The population parameter to be tested is ___________.

A) the average number of 750 customers per day
B) the proportion of customers visiting the dealership per day
C) the mean number of customers visiting the dealership per day
D) the standard deviation of the number of customers visiting the dealership per day

Question 68

The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership.The dealership has historically had 800 customers per day.The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750.Assume that the population standard deviation is 350.To determine whether there has been a decrease in the average number of customers visiting the dealership daily,the appropriate hypotheses are _________.

A)
B)
C)
D)

Question 69

A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50.A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60.The population standard deviation is assumed to equal 0.40.The value of the test statistic is ____________.

A) z = -1.50
B) t₃₅ = -1.50
C) z = 1.50
D) t₃₅ = 1.50

Question 70

The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership.The dealership has historically had 800 customers per day.The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750.Assume that the population standard deviation is 350.The value of the test statistic is ____________.

A) z = -1.429
B) t₉₉ = -1.429
C) z = 1.429
D) t₉₉ = 1.429

Question 71

To test if the mean returns on a major index have changed from the historic monthly average of 1.2%,a sample of 36 recent monthly returns is used to calculate the value of the relevant t_df test statistic.At the 5% level of significance,we reject the null hypothesis if this value is ____________.

A) greater than 1.69
B) greater than 1.645
C) greater than 1.96 or less than −1.96
D) greater than 2.03 or less than −2.03

Question 72

To test if the mean IQ of employees in an organization is greater than 100,a sample of 30 employees is taken and the value of the test statistic is computed as t₂₉ = 2.42 If we choose a 5% significance level,we _____________.

A) reject the null hypothesis and conclude that the mean IQ is greater than 100
B) reject the null hypothesis and conclude that the mean IQ is not greater than 100
C) do not reject the null hypothesis and conclude that the mean IQ is greater than 100
D) do not reject the null hypothesis and conclude that the mean IQ is not greater than 100

Question 73

A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50.A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60.The population standard deviation is assumed to equal 0.40.At a 5% significance level,the critical value(s)is(are)________.

A) 1.645
B) 1.690
C) -1.96 and 1.96
D) -2.030 and 2.030

Question 74

The Boston public school district has had difficulty maintaining on-time bus service for its students ("A Year Later,School Buses Still Late," Boston Globe,October 5,2011).Suppose the district develops a new bus schedule to help combat chronic lateness on a particularly woeful route.Historically,the bus service on the route has been,on average,12 minutes late.After the schedule adjustment,the first 36 runs were an average of eight minutes late.As a result,the Boston public school district claimed that the schedule adjustment was an improvement-students were not as late.Assume a population standard deviation for bus arrival time of 12 minutes.At the 5% significance level,does the evidence support the Boston public school district's claim?

A) No,because the p-value is less thanα.
B) Yes,because the p-value is less than α.
C) No,because the value of the test statistic is greater than the critical value.
D) Yes,because the value of the test statistic is greater than the critical value.

Question 75

The Boston public school district has had difficulty maintaining on-time bus service for its students ("A Year Later,School Buses Still Late," Boston Globe,October 5,2011).Suppose the district develops a new bus schedule to help combat chronic lateness on a particularly woeful route.Historically,the bus service on the route has been,on average,12 minutes late.After the schedule adjustment,the first 36 runs were an average of eight minutes late.As a result,the Boston public school district claimed that the schedule adjustment was an improvement-students were not as late.Assume a population standard deviation for bus arrival time of 12 minutes.Which of the following can be used to determine whether the schedule adjustment reduced the average lateness time of 12 minutes?

A)
B)
C)
D)

Question 76

A recent report claimed that Americans are retiring later in life (U.S.News & World Report,August 17,2011).An economist wishes to determine if the mean retirement age has increased from 62.To conduct the relevant test,she takes a random sample of 38 Americans who have recently retired and computes the value of the test statistic as t₃₇ = 1.92.With α = 0.05,she ____________________________________________________.

A) rejects the null hypothesis and concludes that the mean retirement age has increased
B) rejects the null hypothesis and concludes that the mean retirement age has not increased
C) does not reject the null hypothesis and does not conclude that the mean retirement age has changed
D) does not reject the null hypothesis and does not conclude that the mean retirement age has increased

Question 77

A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50.A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60.The population standard deviation is assumed to equal 0.40.The parameter to be tested is ___________________________.

A) the mean GPA of all university students
B) the mean GPA of the university honors students
C) the mean GPA of 3.60 for the 36 selected honors students
D) the proportion of honors students with a GPA exceeding 3.50

Question 78

An analyst conducts a hypothesis test to check whether the mean return for a particular fund differs from 10%.He assumes that returns are normally distributed and sets up the following competing hypotheses: H_o:μ = 10,H_A:μ ≠ 10 Over the past 10 years the fund has had an average annual return of 13.4% with a standard deviation of 2.6%.The value of the test statistic is 4.14 and the critical values at the 5% significance level are−2.262 and 2.262.The correct decision is to ____________________________________.

A) reject H_o;we can conclude that the mean differs from 10%
B) reject H_o;we cannot conclude that the mean differs from 10%
C) not reject H_o;we can conclude that the mean differs from 10%
D) not reject H_o;we cannot conclude that the mean differs from 10%

Question 79

A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50.A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60.The population standard deviation is assumed to equal 0.40.At a 5% significance level,the decision is to _____________.

A) reject H_o we can conclude that the mean GPA is significantly greater than 3.50
B) reject H_o we cannot conclude that the mean GPA is significantly greater than 3.50
C) not reject H_o we can conclude that the mean GPA is significantly greater than 3.50
D) not reject H_o we cannot conclude that the mean GPA is significantly greater than 3.50

Question 80

A 99% confidence interval for the population mean yields the following results: [−3.79,5.86].At the 1% significance level,what decision should be made regarding the following hypothesis test with H_o:μ = 0,H_A:μ ≠ 0?

A) Reject H_o;we can conclude that the mean differs from zero.
B) Reject H_o;we cannot conclude that the mean differs from zero.
C) Do not reject H_o;we can conclude that the mean differs from zero.
D) Do not reject H_o;we cannot conclude that the mean differs from zero.