Deck 8: Inferences Based on a Single

Question 1

A revenue department is under orders to reduce the time small business owners spend filling out pension form ABC-5500. Previously the average time spent on the form was 6.3 hours. In order to
Test whether the time to fill out the form has been reduced, a sample of 48 small business owners
Who annually complete the form was randomly chosen, and their completion times recorded. The
Mean completion time for ABC-5500 form was 5.7 hours with a standard deviation of 1.8 hours. In
Order to test that the time to complete the form has been reduced, state the appropriate null and
Alternative hypotheses.

Answer 1

B

Question 2

An insurance company sets up a statistical test with a null hypothesis that the average time for processing a claim is 7 days, and an alternative hypothesis that the average time for processing a
Claim is greater than 7 days. After completing the statistical test, it is concluded that the average
Time exceeds 7 days. However, it is eventually learned that the mean process time is really 7 days.
What type of error occurred in the statistical test?

A)Type II error
B)No error occurred in the statistical sense.
C)Type III error
D)Type I error

Answer 2

D

Question 3

Answer 3

To determine if the mean yield for the soybeans differs from 528 bushels per acre,
we test:

Question 4

The null hypothesis represents the status quo to the party performing the sampling experiment.

Question 5

How many tissues should a package of tissues contain? Researchers have determined that a person uses an average of 68 tissues during a cold. Suppose a random sample of 2500 people yielded the
Following data on the number of tissues used during a cold: x = 55, s = 23. Identify the null and
Alternative hypothesis for a test to determine if the mean number of tissues used during a cold is
Less than 68.

A)H0: μ = 68 vs. Ha: μ > 68
B)H0: μ = 68 vs. Ha: μ < 68
C)H0: μ > 68 vs. Ha: μ ≤ 68
D)H0: μ = 68 vs. Ha: μ ≠ 68

Question 6

Question 7

Question 8

The State Association of Retired Teachers has recently taken flak from some of its members regarding the poor choice of the associationʹs name. The associationʹs by-laws require that more
Than 60 percent of the association must approve a name change. Rather than convene a meeting, it
Is first desired to use a sample to determine if meeting is necessary. Suppose the association
Decided to conduct a test of hypothesis using the following null and alternative hypotheses: Define a Type I Error in the context of this problem.

A)They conclude that exactly 60% of the association wants a name change when that is, in fact, true.
B)They conclude that more than 60% of the association wants a name change when, in fact, that is not true.
C)They conclude that more than 60% of the association wants a name change when that is, in fact, true.
D)They conclude that exactly 60% of the association wants a name change when, in fact, that is not true.

Question 9

A method currently used by doctors to screen women for possible breast cancer fails to
detect cancer in 20% of women who actually have the disease. A new method has been
developed that researchers hope will be able to detect cancer more accurately. A random
sample of 90 women known to have breast cancer were screened using the new method.
Of these, the new method failed to detect cancer in eight. Specify the null and alternative
hypotheses that the researchers wish to test.

Question 10

Question 11

Question 12

A __________ is a numerical quantity computed from the data of a sample and is used in reaching a decision on whether or not to reject the null hypothesis.

A)significance level
B)critical value
C)parameter
D)test statistic

Question 13

Question 14

of

Question 15

Question 16

Question 17

Question 18

Question 19

A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful only if the average time
Spent on a delivery does not exceed 38 minutes. The owner has randomly selected 27 customers
And delivered pizzas to their homes. What hypotheses should the owner test to demonstrate that
The pizza delivery will not be successful?

Question 20

The alternative hypothesis is accepted as true unless there is overwhelming evidence that it is false.

Question 21

Solve the problem.

Question 22

Question 23

In a test of hypothesis, the sampling distribution of the test statistic is calculated under the
assumption that the alternative hypothesis is true.

Question 24

For the given rejection region, sketch the sampling distribution for z and indicate the location of the rejection region.
z < -1.96

Question 25

For the given rejection region, sketch the sampling distribution for z and indicate the location of the rejection region.
z < -2.33 or z > 2.33

Question 26

Question 27

Solve the problem.
A rejection region is established in each tail of the sampling distribution for a two-tailed test.

Question 28

Question 29

For the given rejection region, sketch the sampling distribution for z and indicate the location of the rejection region.
z < -1.28

Question 30

Solve the problem.
Consider the following printout.

Question 31

Question 32

Solve the problem.

Question 33

A Type I error occurs when we accept a false null hypothesis.

Question 34

For the given rejection region, sketch the sampling distribution for z and indicate the location of the rejection region.
z > 2.575

Question 35

Question 36

For the given rejection region, sketch the sampling distribution for z and indicate the location of the rejection region.
z < -1.96 or z > 1.96

Question 37

The rejection region refers to the values of the test statistic for which we will reject the alternative
hypothesis.

Question 38

The State Association of Retired Teachers has recently taken flak from some of its members regarding the poor choice of the associationʹs name. The associationʹs by-laws require that more
Than 60 percent of the association must approve a name change. Rather than convene a meeting, it
Is first desired to use a sample to determine if meeting is necessary. Suppose the association
Decided to conduct a test of hypothesis using the following null and alternative hypotheses: Define a Type II Error in the context of this problem.

A)They conclude that exactly 60% of the association wants a name change when, in fact, that is not true.
B)They conclude that more than 60% of the association wants a name change when that is, in fact, true.
C)They conclude that more than 60% of the association wants a name change when, in fact, that is not true.
D)They conclude that exactly 60% of the association wants a name change when that is, in fact, true.

Question 39

Question 40

Solve the problem.

Question 41

Question 42

Question 43

Question 44

A bottling company produces bottles that hold 12 ounces of liquid. Periodically, the company gets complaints that their bottles are not holding enough liquid. To test this claim, the bottling
Company randomly samples 64 bottles and finds the average amount of liquid held by the bottles
Is 11.9155 ounces with a standard deviation of 0.40 ounce. Suppose the p-value of this test is
0.0455. State the proper conclusion.

Question 45

Question 46

Question 47

Question 48

Consider the following printout.

Question 49

A consumer product magazine recently ran a story concerning the increasing prices of digital cameras. The story stated that digital camera prices dipped a couple of years ago, but now are
Beginning to increase in price because of added features. According to the story, the average price
Of all digital cameras a couple of years ago was $215.00. A random sample of cameras was recently
Taken and entered into a spreadsheet. It was desired to test to determine if that average price of all
Digital cameras is now more than $215.00. The information was entered into a spreadsheet and the
Following printout was obtained:

Question 50

Question 51

The smaller the p-value in a test of hypothesis, the more significant the results are.

Question 52

A large university is interested in learning about the average time it takes students to drive to campus. The university sampled 238 students and asked each to provide the amount of time they
Spent traveling to campus. This variable, travel time, was then used conduct a test of hypothesis.
The goal was to determine if the average travel time of all the universityʹs students differed from
20 minutes. Suppose the large-sample test statistic was calculated to be z = 2.14. Find the p-value
For this test of hypothesis.

A)p = 0.4838
B)p = 0.9838
C)p = 0.0324
D)p = 0.0162

Question 53

Question 54

A large university is interested in learning about the average time it takes students to drive to campus. The university sampled 238 students and asked each to provide the amount of time they
Spent traveling to campus. This variable, travel time, was then used to create a confidence interval
And to conduct a test of hypothesis, both of which are shown in the printout below.

Question 55

Question 56

Question 57

Question 58

Based on the information in the screen below, what would you conclude in the test of

Question 59

Question 60

Solve the problem.
The rejection region for a two-tailed test with α = .05 is -1.96 < z < 1.96.

Question 61

Consider the following printout.

Question 62

Question 63

A large university is interested in learning about the average time it takes students to drive to campus. The university sampled 238 students and asked each to provide the amount of time they
Spent traveling to campus. This variable, travel time, was then used conduct a test of hypothesis.
The goal was to determine if the average travel time of all the universityʹs students differed from
20 minutes. Suppose the sample mean and sample standard deviation were calculated to be 23.2
And 20.26 minutes, respectively. Calculate the value of the test statistic to be used in the test.

A)z = 2.437
B)z = 0.173
C)z = 2.551
D)z = 37.59

Question 64

Question 65

Question 66

Question 67

Question 68

Question 69

A local eat-in pizza restaurant wants to investigate the possibility of starting to deliver pizzas. The owner of the store has determined that home delivery will be successful only if the average time
Spent on a delivery does not exceed 27 minutes. The owner has randomly selected 17 customers
And delivered pizzas to their homes in order to test whether the mean delivery time actually
Exceeds 27 minutes. What assumption is necessary for this test to be valid?

A)The population variance must equal the population mean.
B)The sample mean delivery time must equal the population mean delivery time.
C)None. The Central Limit Theorem makes any assumptions unnecessary.
D)The population of delivery times must have a normal distribution.

Question 70

Question 71

The scores on a standardized test are reported by the testing agency to have a mean of 75.
Based on his personal observations, a school guidance counselor believes the mean score is
much higher. He collects the following scores from a sample of 50 randomly chosen
students who took the test.

Question 72

Question 73

A consumer product magazine recently ran a story concerning the increasing prices of digital cameras. The story stated that digital camera prices dipped a couple of years ago, but now are
Beginning to increase in price because of added features. According to the story, the average price
Of all digital cameras a couple of years ago was $215.00. A random sample of n = 200 cameras was
Recently taken and entered into a spreadsheet. It was desired to test to determine if that average
Price of all digital cameras is now more than $215.00. Find the large-sample rejection region
Appropriate for this test if we are using

Question 74

The scores on a standardized test are reported by the testing agency to have a mean of 70.
Based on his personal observations, a school guidance counselor believes the mean score is
much higher. He collects the following scores from a sample of 50 randomly chosen
students who took the test.

Question 75

A supermarket sells rotisserie chicken at a fixed price per chicken rather than by the
weight of the chicken. The store advertises that the average weight of their chickens is 4.6
pounds. A random sample of 30 of the storeʹs chickens yielded the weights (in pounds)
shown below.

Question 76

Question 77

Question 78

Question 79

Question 80

A supermarket sells rotisserie chicken at a fixed price per chicken rather than by the
weight of the chicken. The store advertises that the average weight of their chickens is 4.6
pounds. A random sample of 30 of the storeʹs chickens yielded the weights (in pounds)
shown below.