Question 1

Which of the following meets the requirements of a stratified random sample?

Accepted Answer

A)  A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include six people who volunteer for the sample. 
B)  A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include six people chosen at random, without regard to age. 
C)  A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include six males chosen at random, without regard to age. 
D)  A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include two people chosen at random under the age of 25 and four people chosen at random over 25. 
A)  A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include six people who volunteer for the sample. 
B)  A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include six people chosen at random, without regard to age. 
C)  A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include six males chosen at random, without regard to age. 
D)  A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include two people chosen at random under the age of 25 and four people chosen at random over 25. D

Question 2

A gym knows that each member, on average, spends 70 minutes at the gym per week, with a standard deviation of 20 minutes. Assume the amount of time each customer spends at the gym is normally distributed.
A) What is the probability that a randomly selected customer spends less than 65 minutes at the gym?
B) Suppose the gym surveys a random sample of 49 members about the amount of time they spend at the gym each week. What are the expected value and standard deviation (standard error) of the sample mean of the time spent at the gym?
C) If 49 members are randomly selected, what is the probability that the average time spent at the gym exceeds 75 minutes?

Accepted Answer

a. 0.4013
b. 70 and 2.8571
c. 0.0401

Question 3

Susan has been on a bowling team for 14 years. After examining all of her scores over that period of time, she finds that they follow a normal distribution. Her average score is 225, with a standard deviation of 13. What is the probability that in a one-game playoff, her score is more than 227?

Accepted Answer

A)  0.2676 
B)  0.4389 
C)  0.5596 
D)  0.7324 
A)  0.2676 
B)  0.4389 
C)  0.5596 
D)  0.7324 B

Question 4

A local company makes snack-size bags of potato chips. The company produces batches of 400 snack-size bags using a process designed to fill each bag with an average of 2 ounces of potato chips. However, due to imperfect technology, the actual amount placed in a given bag varies. Assume the population of filling weights is normally distributed with a standard deviation of 0.1 ounce. The company periodically weighs samples of 10 bags to ensure the proper filling process. The last five sample means, in ounces, were 1.99, 2.02, 2.07, 1.96, and 2.01. Is the production process under control?

Accepted Answer

A)  No, because the sample means show a downward trend. 
B)  Yes, because the sample means show a downward trend. 
C)  No, because the sample means fall within the upper and lower control limits. 
D)  Yes, because the sample means fall within the upper and lower control limits. 
A)  No, because the sample means show a downward trend. 
B)  Yes, because the sample means show a downward trend. 
C)  No, because the sample means fall within the upper and lower control limits. 
D)  Yes, because the sample means fall within the upper and lower control limits.

Question 5

The ________ of   is the same as the mean of the individual observations.

Accepted Answer

The answer of The ________ of   is the...

Question 6

A book publisher knows that it takes an average of nine business days from when the material for the book is finalized until the first edition is printed and ready to sell. Suppose the exact amount of time has a standard deviation of four days.
A) Suppose the publisher examines the printing time for a sample of 36 books. What is the probability that the sample mean time is shorter than eight days?
B) Suppose the publisher examines the printing time for a sample of 36 books. What is the probability that the sample mean time is between 7 and 10 days?
C) Suppose the publisher signs a contract for the printer to print 100 books. If the average printing time for the 100 books is longer than 9.3 days, the printer must pay a penalty. What is the probability the penalty clause will be activated?
D) Suppose the publisher signs a contract for the printer to print 10 books. If the average printing time for the 10 books is longer than 9.7 days, the printer must pay a penalty. What is the probability the penalty clause will be activated?

Accepted Answer

a. 0.0668
b. 0.9318

Question 7

Professor Elderman has given the same multiple-choice final exam in his Principles of Microeconomics class for many years. After examining his records from the past 10 years, he finds that the scores have a mean of 76 and a standard deviation of 12. What is the probability that a class of 36 students will have an average greater than 70 on Professor Elderman's final exam?

Accepted Answer

A)  0.0014 
B)  0.3085 
C)  0.6915 
D)  0.9986 
A)  0.0014 
B)  0.3085 
C)  0.6915 
D)  0.9986

Question 8

A packaging company strives to maintain a constant temperature for its packages that require a specific temperature range. It is believed that the temperature of packages follows a normal distribution with a mean of 5 degrees Celsius and a standard deviation of 0.3 degree Celsius. Inspectors take weekly samples for 5 weeks of eight randomly selected boxes and report their temperatures. The five weekly sample means are shown in the table below.   How many points are outside the control limits?

Accepted Answer

A)  1 
B)  2 
C)  3 
D)  4 
A)  1 
B)  2 
C)  3 
D)  4

Question 9

What is the relationship between the standard deviation of the sample mean and the population standard deviation?

Accepted Answer

A)  se(   ) =   
B)  se(   ) =   
C)  se(   ) =   
D)  se(   ) =   
A)  se(   ) =   
B)  se(   ) =   
C)  se(   ) =   
D)  se(   ) =

Question 10

Professor Elderman has given the same multiple-choice final exam in his Principles of Microeconomics class for many years. After examining his records from the past 10 years, he finds that the scores have a mean of 76 and a standard deviation of 12. What is the probability Professor Elderman's class of 36 has a class average below 78?

Accepted Answer

A)  0.1587 
B)  0.5675 
C)  0.8413 
D)  Cannot be determined. 
A)  0.1587 
B)  0.5675 
C)  0.8413 
D)  Cannot be determined.

Question 11

According to the recent report, scientists in New England say they have identified a set of genetic variants that predicts extreme longevity with 77% accuracy. Assume 150 patients decide to get their genome sequenced. If the claim by scientists is accurate, what is the probability that more than 120 patients will get a correct diagnosis for extreme longevity?

Accepted Answer

A)  0.5151 
B)  0.2219 
C)  0.1515 
D)  0.1913 
A)  0.5151 
B)  0.2219 
C)  0.1515 
D)  0.1913

Question 12

Super Bowl XLVI was played between the New York Giants and the New England Patriots in Indianapolis. Due to a decade-long rivalry between the Patriots and the city's own team, the Colts, most Indianapolis residents were rooting heartily for the Giants. Suppose that 90% of Indianapolis residents wanted the Giants to beat the Patriots. What is the probability that, of a sample of 100 Indianapolis residents, at least 15% were rooting for the Patriots in Super Bowl XLVI?

Accepted Answer

A)  0.0300 
B)  0.0478 
C)  0.4763 
D)  0.9525 
A)  0.0300 
B)  0.0478 
C)  0.4763 
D)  0.9525

Question 13

Professor Elderman has given the same multiple-choice final exam in his Principles of Microeconomics class for many years. After examining his records from the past 10 years, he finds that the scores have a mean of 76 and a standard deviation of 12. What is the probability that a class of 15 students will have a class average greater than 70 on Professor Elderman's final exam?

Accepted Answer

A)  0.0262 
B)  0.6915 
C)  0.9738 
D)  Cannot be determined. 
A)  0.0262 
B)  0.6915 
C)  0.9738 
D)  Cannot be determined.

Question 14

Suppose that, on average, electricians earn approximately µ = $54,000 per year in the United States. Assume that the distribution for electricians' yearly earnings is normally distributed and that the standard deviation is σ = $12,000. Given a sample of four electricians, what is the standard deviation for the sampling distribution of the sample mean?

Accepted Answer

A)  6,000 
B)  12,000 
C)  36,000 
D)  54,000 
A)  6,000 
B)  12,000 
C)  36,000 
D)  54,000

Question 15

A university administrator expects that 25% of students in a core course will receive an A. He looks at the grades assigned to 60 students. What are the expected value and the standard error for the proportion of students that receive an A?

Accepted Answer

A)  0.25 and 0.0031 
B)  0.25 and 0.0559 
C)  15.0 and 0.0031 
D)  15.0 and 0.0559 
A)  0.25 and 0.0031 
B)  0.25 and 0.0559 
C)  15.0 and 0.0031 
D)  15.0 and 0.0559

Question 16

It is known that college students at a local community college study 12 hours per week with a standard deviation of five hours. What are the expected value and variance for a sample of nine students?

Accepted Answer

Expected value equal

Question 17

For any population X with expected value µ and standard deviation σ, the sampling distribution of   will be approximately normal if the sample size n is sufficiently small. As a general guideline, the normal distribution approximation is justified when n < 30.

Accepted Answer

A) True 
 B)False

Question 18

A random sample of size 36 is taken from a population with mean µ = 17 and standard deviation σ = 6. The probability that the sample mean is between 15 and 18 is ________.

Accepted Answer

A)  0.0228 
B)  0.8186 
C)  0.8413 
D)  0.8641 
A)  0.0228 
B)  0.8186 
C)  0.8413 
D)  0.8641

Question 19

According to the recent report, scientists in New England say they have identified a set of genetic variants that predicts extreme longevity with 77% accuracy. Assume 150 patients decide to get their genome sequenced. If the claim by scientists is accurate, what is the probability that fewer than 70% of the patients will get a correct diagnosis for extreme longevity?

Accepted Answer

A)  0.1422 
B)  0.0722 
C)  0.2214 
D)  0.0208 
A)  0.1422 
B)  0.0722 
C)  0.2214 
D)  0.0208

Question 20

In any production process, variation in the quality of the end product is inevitable. Chance variation, or common variation, refers to ________.

Accepted Answer

A)  the variation caused by stratified random sampling 
B)  the variation caused by the use of the finite correction factor 
C)  specific events or factors that can usually be identified and eliminated 
D)  a number of randomly occurring events that are part of the production process 
A)  the variation caused by stratified random sampling 
B)  the variation caused by the use of the finite correction factor 
C)  specific events or factors that can usually be identified and eliminated 
D)  a number of randomly occurring events that are part of the production process

Which of the following meets the requirements of a stratified random sample?

Susan has been on a bowling team for 14 years. After examining all of her scores over that period of time, she finds that they follow a normal distribution. Her average score is 225, with a standard deviation of 13. What is the probability that in a one-game playoff, her score is more than 227?

The ________ of is the same as the mean of the individual observations.

What is the relationship between the standard deviation of the sample mean and the population standard deviation?

A university administrator expects that 25% of students in a core course will receive an A. He looks at the grades assigned to 60 students. What are the expected value and the standard error for the proportion of students that receive an A?

It is known that college students at a local community college study 12 hours per week with a standard deviation of five hours. What are the expected value and variance for a sample of nine students?

For any population X with expected value µ and standard deviation σ, the sampling distribution of will be approximately normal if the sample size n is sufficiently small. As a general guideline, the normal distribution approximation is justified when n < 30.

A random sample of size 36 is taken from a population with mean µ = 17 and standard deviation σ = 6. The probability that the sample mean is between 15 and 18 is ________.

In any production process, variation in the quality of the end product is inevitable. Chance variation, or common variation, refers to ________.

Statistics and Data

Tabular and Graphical Methods

Numerical Descriptive Measures

Introduction to Probability

Discrete Probability Distributions

Continuous Probability Distributions

Interval Estimation

Hypothesis Testing

Statistical Inference Concerning Two Populations

Statistical Inference Concerning Variance

Chi-Square Tests

Analysis of Variance

Regression Analysis

Inference With Regression Models

Regression Models for Nonlinear Relationships

Regression Models With Dummy Variables

Time Series and Forecasting

Returns, Index Numbers, and Inflation

Nonparametric Tests

Filters

Exam 7: Sampling and Sampling Distributions

Which of the following meets the requirements of a stratified random sample?

Susan has been on a bowling team for 14 years. After examining all of her scores over that period of time, she finds that they follow a normal distribution. Her average score is 225, with a standard deviation of 13. What is the probability that in a one-game playoff, her score is more than 227?

The ________ of is the same as the mean of the individual observations.

What is the relationship between the standard deviation of the sample mean and the population standard deviation?

A university administrator expects that 25% of students in a core course will receive an A. He looks at the grades assigned to 60 students. What are the expected value and the standard error for the proportion of students that receive an A?

It is known that college students at a local community college study 12 hours per week with a standard deviation of five hours. What are the expected value and variance for a sample of nine students?

For any population X with expected value µ and standard deviation σ, the sampling distribution of will be approximately normal if the sample size n is sufficiently small. As a general guideline, the normal distribution approximation is justified when n < 30.

A random sample of size 36 is taken from a population with mean µ = 17 and standard deviation σ = 6. The probability that the sample mean is between 15 and 18 is ________.

In any production process, variation in the quality of the end product is inevitable. Chance variation, or common variation, refers to ________.

Statistics and Data

Tabular and Graphical Methods

Numerical Descriptive Measures

Introduction to Probability

Discrete Probability Distributions

Continuous Probability Distributions

Interval Estimation

Hypothesis Testing

Statistical Inference Concerning Two Populations

Statistical Inference Concerning Variance

Chi-Square Tests

Analysis of Variance

Regression Analysis

Inference With Regression Models

Regression Models for Nonlinear Relationships

Regression Models With Dummy Variables

Time Series and Forecasting

Returns, Index Numbers, and Inflation

Nonparametric Tests

Filters