Questions and Answers of Fundamentals Of Statistics

The standard deviation of the sampling distribution of x̅, σx̅, is called the____________ of the___________.
Under what conditions is the sampling distribution of p̆ approximately normal?
According to the U.S. Census Bureau, in 2009, 10% of adults 25 years and older in the United States had advanced degrees. A researcher with the U.S. Department of Education surveys 500 randomly
Bicycle sharing exists in a variety of cities around the country. Los Angeles has the Metro Bike Share system. Users pick up a bike from one station, go for a ride, and return the bike to any
State the Central Limit Theorem.
Suppose you want to study the number of hours of sleep you get each evening. To do so, you look at the calendar and randomly select 10 days out of the next 300 days and record the number of hours you
One of the biggest purchases we make in our lifetimes is for a home. Questions that we all ask are these:• How much should I spend for a particular home?• How many bathrooms are there?• How
Define each of the following.(a) Point estimate(b) Confidence interval(c) Level of confidence(d) Margin of error
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?
What does the 95% represent in a 95% confidence interval?
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
If a sample proportion is 0.55, which of the following could be a 90% confidence interval for the population proportion? Select all that apply.(a) Lower bound: 0.50; Upper bound: 0.60(b) Lower bound:
A tennis enthusiast wants to estimate the mean length of men’s singles matches held during the Wimbledon tennis tournament. From the Wimbledon history archives, he randomly selects 40 matches
Self-driving vehicles periodically suffer from a disengagement of the self-driving feature. In these cases, it is important to know how long it takes for the driver to manually take control of the
In Problems, determine the point estimate of the population mean and margin of error for each confidence interval.Lower bound: 18, upper bound: 24
In Problems, determine the point estimate of the population mean and margin of error for each confidence interval.Lower bound: 20, upper bound: 30
A simple random sample of size n is drawn. The sample mean, x̅, 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 μ if the
Go to www.pearsonhighered.com/ sullivanstats to obtain the data file 9_4_21. The data represent the status of licenses for short-term rentals in New Orleans, where “Yes” indicates the license is
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
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
In Problems, determine the point estimate of the population mean and margin of error for each confidence interval.Lower bound: 5, upper bound: 23
In Problems, determine the point estimate of the population mean and margin of error for each confidence interval.Lower bound: 15, upper bound: 35
A simple random sample of size n is drawn from a population that is normally distributed. The sample mean, x̅, is found to be 108, and the sample standard deviation, s, is found to be 10.(a)
A simple random sample of size n is drawn from a population that is normally distributed. The sample means, x̅, is found to be 50, and the sample standard deviation, s, is found to be 8.(a)
A simple random sample of size n is drawn. The sample means, x̅, is found to be 18.4, and the sample standard deviation, s, is found to be 4.5.(a) Construct a 95% confidence interval for μ if the
The following data represent the property tax for a random sample of 50 single-family homes in the city of Houston. Suppose you want to estimate the typical property real estate tax for a
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
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
Explain what “95% confidence” means in a 95% confidence interval.
In Problems find the value of za.z0.02
Suppose that polls suggest a candidate in a local school board election has 52% of the voters in favor of her as the candidate.(a) Explain how you could use the integers from 1 to 100 to simulate
In Problems find the value of za.z0.025
In Problems find the value of za.z0.15
Find the value of z0.04.
What are the properties of the normal density curve?
In an election for President of the United States, a pollster wishes to predict the winner of the popular vote. She will do this by taking a random sample of 1000 voters and ask each to disclose who
Suppose you would like to estimate the number of rolls it typically takes before observing a seven when rolling a pair of fair dice.(a) Explain how you might use simulation to determine the typical
In Problems find the value of each factorial.7!
Recently, Pew Research reported that the proportion of adult Americans aged 18 or older who believe online dating is a good way to meet people is 0.59. There are approximately 241,000,000 Americans
In Problems find the value of each factorial.10!
Recently, the Gallup Organization reported that the proportion of adult Americans aged 18 years or older who believe the state of moral values in the country is getting worse is 0.77. There are
In Problems find the value of each factorial.12!
Suppose that we add the Dodge Viper to the data in Problem 24 in Section 4.2. A Dodge Viper weighs 3425 pounds and gets 11 miles per gallon. Compute the coefficient of determination of the expanded
Go to www.pearsonhighered.com/sullivanstats to obtain the data file 4_3_17. The data represent the 2015 tax rate per pack of cigarettes and the percent of cigarettes smuggled as a percentage of total
Everyone knows that alcohol impairs reaction time. For example, one study indicates that reaction time at a blood alcohol concentration of 0.08% doubles from 1.5 to 3 seconds. Your job is to compile
Define each of the following.(a) Probability (b) Experiment(c) Event (d) Sample space(e) Equally likely outcomes (f) Impossible event(g) Unusual event
An interesting problem from probability is the birthday problem. The problem deals with determining the likelihood that at least two people share the same birthday in a room of n individuals. The
If P(E) = 0.6 and P(E|F)= 0.34, are events E and F independent?
Craps is a popular casino game. In its most basic form, two dice are initially thrown. If the outcome of the roll is 2, 3, o 12 (that is, the sum of the two die is 2, 3, or 12), the player loses his
In the game show The Price Is Right, two players get to spin a wheel with the values 05, 10, 15, . . . . , 95, 100 on it. In the game, Player 1 spins the wheel one time and gets to decide whether
Suppose that E and F are two events and that P(E and F) = 0.21 and P(E) = 0.4. What is P(F|E)?
In Problems find the value of each factorial.5!
Mammograms are used to detect breast cancer. Suppose a mammogram is known to be 80% accurate, which means P(positive mammogram|cancer) = 0.80. Suppose in the United States, 40 million women are
The music player on an iPhone plays each of 10 songs. Once a song is played, it is not repeated until all the songs have been played. In how many different ways can the player play the 10 songs?
Your daily commute to work requires that you cross railroad tracks. At this particular railroad crossing the trains tend to be long and slow. So, getting stopped by a train will likely make you late
On your drives to school each day you feel like there is a light that is always red when you reach it. You decide to record data to determine the likelihood of arriving at the light while it is
According to the U.S. Census Bureau, the probability that a randomly selected worker primarily drives a car to work is 0.764. The probability that a randomly selected worker primarily takes public
Companies whose stocks are listed on the NASDAQ stock exchange have their company name represented by either four or five letters (repetition of letters is allowed). What is the maximum number of
The following data represent the number of drivers involved in a fatal crash in 2016 in various light and weather conditions.(a) Determine the probability that a randomly selected fatal crash in 2016
Is there a “path” to success? Brookings scholars Ron Haskins and Isabel Sawhill suggest the path to success is: education, followed by work, followed by marriage, followed by children.
(a) In 2017, the median income of families in the United States was $60,336. What is the probability that a randomly selected family has an income greater than $60,336?(b) The middle 50% of enrolled
A woman who was shopping in Los Angeles had her purse stolen by a young, blonde female who was wearing a ponytail. The blonde female got into a yellow car that was driven by a black male who had a
At the Wimbledon Tennis Championship, to win a match in men’s singles a player must win the best of five sets. The following data represent the number of sets played, X, in the men’s singles
Let’s say a player typically gets a hit in 3 out of every 10 at-bats (for a 0.300 batting average). Suppose the player has not had a hit in his previous four at-bats. In baseball, you will often
The following is a quote by Pierre-Simon Laplace: “To discover the best treatment to use in curing a disease, it is sufficient to test each treatment on the same number of patients, while keeping
A friend of yours regularly plays the lottery but has never won. She says that she feels really good about this weekend’s drawing because she is due for a winning ticket. Explain the flaw in your
The following data represent the number of games played in each World Series from 1923 to 2018.In Problems (a) construct a discrete probability distribution for the random variable(b) draw a
What is a random variable?
Consider a binomial probability distribution with parameters n = 8 and p = 0.75.(a) Construct a binomial probability distribution with these parameters.(b) Compute the mean and standard deviation of
The following table shows the net winnings from a $1 bet in a video poker game.(a) Compute and interpret the expected net winnings from the player’s point of view. Round your answer to three
Consider a binomial probability distribution with parameters n = 5 and p = 0.2.(a) Construct a binomial probability distribution with these parameters.(b) Compute the mean and standard deviation of
A major theme during the 2018 election in both the House and Senate was the popularity of President Trump (a Republican). The scatter diagram below shows the presidential approval rating
After scoring a touchdown in football, the scoring team is entitled to either earn 1 extra point (by kicking the ball through goal posts) or 2 extra points (by advancing the ball past the goal line).
Toxic Epidermal Necrolysis (TEN), also known as Lyell’s syndrome, is a life-threatening disease characterized by blisters that cover the skin and extensive peeling off of the skin. In a
You are interested in modeling the behavior of stocks. In particular, you want to build a model that describes the rate of return on a basket of stocks, such as large capitalization
Find the value of z0.20.
What are the two properties that a probability density function must satisfy?
In Problems find the value of za.z0.01
In a Pew Research poll, 42% of adult Americans had a positive view of socialism. You conduct a survey of 200 randomly selected students at your school and find that 103 have a positive view of
The length of a 4-year-old male’s upper arm is approximately normally distributed with mean μ = 21.8 cm and standard deviation σ = 2.0 cm.(a) Draw a normal curve with the parameters
The length of a 10-year-old female’s upper leg is approximately normally distributed with mean μ = 33.8 cm and standard deviation σ = 2.1 cm.(a) Draw a normal curve with the parameters
The ability to determine the age of some individuals can be difficult if there are not quality government records of birth. Bone growth takes place at the growth plates at the end of long bones. Once
In Problems find the value of each factorial.0!
In Problems evaluate each expression.6!2!/4!
In Problems find the value of each factorial.1!
In Problems evaluate each expression.7P3
In Problems find the value of each permutation.6P2
In Problems evaluate each expression.9C4
In Problems find the value of each permutation.7P2
During the 2018 season, the Chicago Cubs won 58% of their games. Assuming that the outcomes of the baseball games are independent and that the percentage of wins this season will be the same as in
In Problems find the value of each permutation.4P4
According to Pew Research, in 27% of marriages, the woman has a bachelor’s degree and the marriage lasts at least 20 years. According to the Census Bureau, 35% of women have a bachelor’s degree.
The following data represent the birth weights (in grams) of babies born in 2017, along with the period of gestation.(a) What is the probability that a randomly selected baby born in 2017 was
In Problems find the value of each permutation.7P7
In Problems find the value of each permutation.5P0
In Problems find the value of each permutation.4P0
In Problems find the value of each permutation.8P3
The following data represent the number of drivers involved in a fatal crash in 2016 in various light and weather conditions.(a) Among fatal crashes in normal weather, what is the probability that a
In 1970, 92% of American 30-year-olds earned more than their parents did at age 30 (adjusted for inflation). In 2014, only 51% of American 30-year-olds earned more than their parents did at age
In Problems find the value of each permutation.9P4

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