Question: A simple random sample of size n

> A simple random sample of size n = 17 is drawn from a population that is normally distributed. The sample mean is found to be / = 3.25, and the sample standard deviation is found to be s = 1.17. Construct a 95% confidence interval for the population mean

> Research the origins of the Gallup Poll and the current sampling method the organization uses. Report your findings to the class.

> A simple random sample of size n = 12 is drawn from a population that is normally distributed. The sample mean is found to be / = 45, and the sample standard deviation is found to be s = 14. Construct a 90% confidence interval for the population mean.

> A simple random sample of size n = 785 adults was asked if they follow college football. Of the 785 surveyed, 275 responded that they did follow college football. Construct a 95% confidence interval for the population proportion of adults who follow coll

> A simple random sample of size n = 300 individuals who are currently employed is asked if they work at home at least once per week. Of the 300 employed individuals surveyed, 35 responded that they did work at home at least once per week. Construct a 99%

> What requirements must be satisfied in order to construct a confidence interval about a population mean?

> Put the following in order from least to greatest. • t0.10 with 5 degrees of freedom • t0.10 with 15 degrees of freedom • z0.10

> State the properties of Student’s t-distribution.

> The notation ta is the t-value such that the area under the t-distribution to the right of ta is______ .

> As the number of degrees of freedom in the t-distribution increases, the spread of the distribution________ (increases/ decreases).

> Population A has standard deviation / and population B has standard deviation /How many times larger than Population A’s sample size does Population B’s need to be to estimate  with the same margin of error? (Hint: Compute /

> Suppose you have two populations: Population A—All students at Illinois State University (N = 21,000) and Population B—All residents of the city of Homer Glen, IL (N = 21,000). You want to estimate the mean age of each population using two separate sampl

> What is random sampling? Why is it necessary for a sample to be obtained randomly rather than conveniently? Will randomness guarantee that a sample will provide accurate information about the population? Explain.

> The mean age of the 45 presidents of the United States (as of 2018) on the day of inauguration is 55.0 years, with a standard deviation of 6.6 years. A researcher constructed a 95% confidence interval for the mean age of presidents on inauguration day. H

> Explain what is meant by degrees of freedom.

> The procedure for constructing a t-interval is robust. Explain what this means.

> Explain why the t-distribution has less spread as the number of degrees of freedom increases.

> A question on the General Social Survey was, “When you drink, how many drinks do you have?” The survey was administered to a random sample of 243 adult Americans aged 21 or older. Go to www.pearsonhighered.com/ sullivanstats to obtain the data file 9_2_4

> Researchers Havar Brendryen and Pal Kraft conducted a study in which 396 subjects were randomly assigned to either an experimental smoking cessation program or control group. The experimental program consisted of the Internet and phone-based Happy Ending

> The exponential probability distribution can be used to model waiting time in line or the lifetime of electronic components. Its density function is skewed right. Suppose the wait-time in a line can be modeled by the exponential distribution with  =  =

> IQ scores based on the Wechsler Intelligence Scale for Children (WISC) are known to be approximately normally distributed with  = 100 and =15. (a) Use StatCrunch, Minitab, or some other statistical software to simulate obtaining 100 simple random sampl

> The following small data set represents a simple random sample from a population whose mean is 50. (a) A normal probability plot indicates that the data could come from a population that is normally distributed with no outliers. Compute a 95% confidence

> The data sets represent simple random samples from a population whose mean is 100. (a) Compute the sample mean of each data set. (b) For each data set, construct a 95% confidence interval about the population mean. (c) What effect does the sample size n

> Suppose a political strategist wants to get a sense of how American adults aged 18 years or older feel about health care and health insurance. (a) In a political poll, what would be a good frame to use for obtaining a sample? (b) Explain why simple rando

> A researcher wanted to determine the mean number of hours per week (Sunday through Saturday) the typical person watches television. Results from the Sullivan Statistics Survey I indicate that s = 7.5 hours. (a) How many people are needed to estimate the

> A recent Gallup poll asked Americans to disclose the number of books they read during the previous year. Initial survey results indicate that s = 16.6 books. (a) How many subjects are needed to estimate the number of books Americans read the previous yea

> Dr. Paul Oswiecmiski wants to estimate the mean serum HDL cholesterol of all 20- to 29-year-old males. How many subjects are needed to estimate the mean serum HDL cholesterol of all 20- to 29-year-old males within 1.5 points with 90% confidence, assuming

> Dr. Paul Oswiecmiski wants to estimate the mean serum HDL cholesterol of all 20- to 29-year-old females. How many subjects are needed to estimate the mean serum HDL cholesterol of all 20- to 29-year-old females within 2 points with 99% confidence assumin

> The Sullivan Statistics Survey II asks, “What percent of one’s income should an individual pay in federal income taxes?” Go to www.pearsonhighered.com/sullivanstats to obtain the data file SullivanStatsSurveyII using the file format of your choice for th

> The data set “Tornadoes_2017” located at www.pearsonhighered.com/ sullivanstats contains a variety of variables that were measured for all tornadoes in the United States in 2017. (a) Compute the population mean length of a tornado in the United States in

> The trade volume of a stock is the number of shares traded on a given day. The following data, in millions (so that 6.16 represents 6,160,000 shares traded), represent the volume of PepsiCo stock traded for a random sample of 40 trading days in 2018. (a)

> The following data represent the wait time (in minutes) for a random sample of 40 visitors to Disney’s Dinosaur Ride in Animal Kingdom. (a) Draw a relative frequency histogram of the data. Comment on the shape of the distribution. (b) Draw a boxplot of t

> The following data represent the age (in weeks) at which babies first crawl based on a survey of 12 mothers conducted by Essential Baby. (a) Use either Option 1 or Option 2 to verify the requirements for constructing a confidence interval for the populat

> The following data represent the repair cost for a low-impact collision in a simple random sample of mini- and micro-vehicles (such as the Chevrolet Aveo or Mini Cooper). (a) Use either Option 1 or Option 2 to verify the requirements for constructing a c

> A marketing executive for Coca-Cola, Inc., wants to identify television shows that people in the Boston area who typically drink Coke are watching. The executive has a list of all households in the Boston area. Design a sampling method to obtain the indi

> Travelers pay taxes for flying, car rentals, and hotels. The following data represent the total travel tax for a 3-day business trip in 8 randomly selected cities. Note: Chicago travel taxes are the highest in the country at $101.27. A normal probability

> The following data represent the pH of rain for a random sample of 12 rain dates in Tucker County, West Virginia. A normal probability plot suggests the data could come from a population that is normally distributed. A boxplot indicates there are no outl

> A recent Gallup poll asked 1006 Americans, “During the past year, about how many books, either hardcover or paperback, did you read either all or part of the way through?” Results of the survey indicated that / = 13.4 books and s = 16.6 books. Construct

> A Tootsie Pop is a sucker with a candy center. A famous commercial for Tootsie Pops once asked, “How many licks to the center of a Tootsie Pop?” In an attempt to answer this question, Cory Heid of Siena Heights University asked 92 volunteers to count the

> How much time do Americans spend eating or drinking? Suppose for a random sample of 1001 Americans age 15 or older, the mean amount of time spent eating or drinking per day is 1.22 hours with a standard deviation of 0.65 hour. Source: American Time U

> A random sample of 51 fatal crashes in 2017 in which the driver had a positive blood alcohol concentration (BAC) from the National Highway Traffic Safety Administration results in a mean BAC of 0.167 gram per deciliter (g/dL) with a standard deviation of

> Refer to the “Sleeping” results from Problem 22. What could be done to decrease the width of the confidence interval?

> For the “Hours Worked” survey conducted by Gallup in Problem 21, provide two recommendations for decreasing the width of the interval.

> Michael Sullivan, the author of this text, determined the mean amount of weekly screen time spent on his phone was 81.3 minutes. A 95% confidence interval for the mean amount of time spent on his phone weekly has a lower bound of 72.9 minutes. (a) What i

> The trade magazine QSR routinely checks the drive-through service times of fast-food restaurants. A 90% confidence interval that results from examining 607 customers in Taco Bell’s drive-through has a lower bound of 161.5 seconds and an upper bound of 16

> A pharmaceutical company wants to conduct a survey of 30 individuals who have high cholesterol. The company has obtained a list from doctors throughout the country of 6600 individuals who are known to have high cholesterol. Design a sampling method to ob

> A 90% confidence interval for the number of hours that full-time college students sleep during a weekday is lower bound: 7.8 hours and upper bound: 8.8 hours. Which of the following represents a reasonable interpretation of the result? For those that are

> In a survey conducted by the Gallup Organization, 1100 adult Americans were asked how many hours they worked in the previous week. Based on the results, a 95% confidence interval for mean number of hours worked was lower bound: 42.7 hours and upper bound

> A simple random sample of size n is drawn. The sample mean, /, is found to be 35.1, and the sample standard deviation, s, is found to be 8.7. (a) Construct a 90% confidence interval for  if the sample size, n, is 40. (b) Construct a 90% confidence inter

> A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, /, is found to be 50, and the sample standard deviation,s, is found to be 8. (a) Construct a 98% confidence interval for  if the sample size, n, i

> A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, /, is found to be 108, and the sample standard deviation, s, is found to be 10. (a) Construct a 96% confidence interval for  if the sample size, n

> Lower bound: 15, upper bound: 35

> Lower bound: 5, upper bound: 23

> Lower bound: 20, upper bound: 30

> Lower bound: 18, upper bound: 24

> The county sheriff wants to determine if a certain highway has a high proportion of speeders traveling on it. Design a sampling method to obtain the individuals in the sample. Be sure to support your choice.

> Number of unpopped kernels in a bag of microwave popcorn

> n = 9; Correlation = 0.997

> n = 13; Correlation = 0.966

> n = 15; Correlation = 0.893

> n = 12; Correlation = 0.987

> (a) Find the t-value such that the area in the right tail is 0.02 with 19 degrees of freedom. (b) Find the t-value such that the area in the right tail is 0.10 with 32 degrees of freedom. (c) Find the t-value such that the area left of the t-value is 0.0

> (a) Find the t-value such that the area in the right tail is 0.10 with 25 degrees of freedom. (b) Find the t-value such that the area in the right tail is 0.05 with 30 degrees of freedom. (c) Find the t-value such that the area left of the t-value is 0.

> The procedure for constructing a confidence interval about a mean is_____ , which means minor departures from normality do not affect the accuracy of the interval.

> True or False: To construct a confidence interval about the mean, the population from which the sample is drawn must be approximately normal.

> Put the following in order from narrowest to widest interval. Assume the sample size and sample proportion is the same for all four confidence intervals. (a) 95% confidence interval (b) 80% confidence interval (c) 99% confidence interval (d) 90% confiden

> If you constructed one hundred 95% confidence intervals based on one hundred different simple random samples of size n, how many of the intervals would you expect to include the unknown parameter? Assume all model requirements are satisfied.

> Target wants to open a new store in the village of Lockport. Before construction, Target’s marketers want to obtain some demographic information regarding the area under consideration. Design a sampling method to obtain the individuals in the sample. Be

> Define each of the following. (a) Point estimate (b) Confidence interval (c) Level of confidence (d) Margin of error

> The 116th House of Representatives of the United States of America has 435 members, of which 106 are women. An alien lands near the U.S. Capitol and treats members of the House as a random sample of the human race. He reports to his superiors that a 95%

> Two researchers, Jaime and Mariya, are each constructing confidence intervals for the proportion of a population who is left-handed. They find the point estimate is 0.13. Each independently constructed a confidence interval based on the point estimate, b

> Katrina wants to estimate the proportion of adult Americans who read at least 10 books last year. To do so, she obtains a simple random sample of 100 adult Americans and constructs a 95% confidence interval. Matthew also wants to estimate the proportion

> Why do polling companies often survey 1060 individuals when they wish to estimate a population proportion with a margin of error of 3% with 95% confidence?

> Explain why quadrupling the sample size causes the margin of error to be cut in half.

> What type of variable is required to construct a confidence interval for a population proportion?

> Explain what “95% confidence” means in a 95% confidence interval.

> The American Society for Microbiology (ASM) and the Soap and Detergent Association (SDA) jointly commissioned two separate studies, both of which were conducted by Harris Interactive. In one of the studies, 1001 adults were interviewed by telephone an

> Alan wants to estimate the proportion of adults who walk to work. In a survey of 10 adults, he finds 1 who walks to work. Explain why a 95% confidence interval using the normal model yields silly results. Then compute and interpret a 95% confidence inter

> A school board at a local community college is considering raising the student services fees. The board wants to obtain the opinion of the student body before proceeding. Design a sampling method to obtain the individuals in the sample. Be sure to suppor

> Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 20 students, she finds 2 who eat cauliflower. Obtain and interpret a 95% confidence interval for the proportion of students who eat cauliflower on Jane’s

> A Bernoulli random variable is a variable that is either 0 (a failure) or 1 (a success). The probability of success is denoted p. (a) Use a statistical spreadsheet to generate 1000 Bernoulli samples of size n = 20 with p = 0.15. (b) Determine the sample

> CNN polled 702 likely voters immediately preceding the 2018 Arizona senate race. The results of the survey indicated that Kyrsten Sinema had the support of 51% of respondents, while Martha McSally had support of 47%. The poll’s margin of error was 4.4%.

> In a Gallup Poll, 44% of the people polled answered “more strict” to the following question: “Do you feel that the laws covering the sale of firearms should be made more strict, less strict, or kept as they are now?” Suppose the margin of error in the po

> In a Gallup poll, 64% of the people polled answered yes to the following question: “Are you in favor of the death penalty for a person convicted of murder?” The margin of error in the poll was 3%, and the estimate was made with 95% confidence. At least h

> A sociologist wishes to conduct a poll to estimate the percentage of Americans who favor affirmative action programs for women and minorities for admission to colleges and universities. What sample size should be obtained if she wishes the estimate to be

> A television sports commentator wants to estimate the proportion of Americans who follow professional football. What sample size should be obtained if he wants to be within 3 percentage points with 95% confidence if (a) he uses a 2010 estimate of 53% ob

> A school administrator is concerned about the amount of credit-card debt that college students have. She wishes to conduct a poll to estimate the percentage of full-time college students who have credit-card debt of $2000 or more. What size sample should

> A researcher for the U.S. Department of the Treasury wishes to estimate the percentage of Americans who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 2 percentage points with 98% confidence if (a

> An urban economist wishes to estimate the proportion of Americans who own their homes. What size sample should be obtained if he wishes the estimate to be within 0.02 with 90% confidence if (a) he uses a 2010 estimate of 0.669 obtained from the U.S. Cens

> The city of Naperville is considering the construction of a new commuter rail station. The city wishes to survey the residents of the city to obtain their opinion regarding the use of tax dollars for this purpose. Design a sampling method to obtain the i

> A researcher wishes to estimate the proportion of households that have broadband Internet access. What size sample should be obtained if she wishes the estimate to be within 0.03 with 99% confidence if (a) she uses a 2009 estimate of 0.635 obtained from

> Go to www.pearsonhighered.com/ sullivanstats to obtain the data file 9_1_34 using the file format of your choice for the version of the text you are using. The data represent the daily (for example, Monday to Tuesday) movement of Johnson & Johnson (JNJ)

> The data set “Tornadoes_2017” located at www.pearsonhighered.com/ sullivanstats contains a variety of variables that were measured for all tornadoes in the United States in 2017. (a) The F scale is used to describe the range of wind speeds of a tornado.

> The Sullivan Statistics Survey I asks, “Would you be willing to pay higher taxes if the tax revenue went directly toward deficit reduction?” Treat the survey respondents as a random sample of adult Americans. Go to www.pearsonhighered.com/sullivanstats t

> In a survey conducted by the marketing agency 11mark, 241 of 1000 adults 19 years of age or older confessed to bringing and using their cell phone every trip to the bathroom (confessions included texting and answering phone calls). (a) What is the sample

> In a survey of 700 community college students, 481 indicated that they have read a book for personal enjoyment during the school year (based on data from the Community College Survey of Student Engagement). (a) Determine a 90% confidence interval for the

> Low levels of testosterone in adult males may be treated using AndroGel 1.62%. In clinical studies of 234 adult males who were being treated with AndroGel 1.62%, it was found that 26 saw their prostate-specific antigen (PSA) elevated. The PSA is a protei

> In a USA Today/Gallup poll, 768 of 1024 randomly selected adult Americans aged 18 or older stated that a candidate’s positions on the issue of family values are extremely or very important in determining their vote for president. (a) Obtain a point estim

> A random sample of 1003 adult Americans was asked, “Do you pretty much think televisions are a necessity or a luxury you could do without?” Of the 1003 adults surveyed, 521 indicated that televisions are a luxury they could do without. (a) Obtain a point

> Relative to other nations, how do fourth-graders in the United States rank in terms of reading and math ability? Are they in the bottom 50% or in the top 50%? In a survey of 700 randomly sampled registered voters in the United States conducted by Conques