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elementary statistics

Questions and Answers of Elementary Statistics

A study conducted in 2015 by the technology company Rovi (now TiVo) showed that the mean time spent per day browsing the video streaming service Netflix for something to watch was 19.3 minutes.
A random sample of 60 second graders in a certain school district are given a standardized mathematics skills test. The sample mean score is x̄ = 52.Assume the standard deviation of test scores is
Are older men shorter than younger men?According to the National Health Statistics Reports, the mean height for U.S. men is 69.4 inches. In a sample of 300 men between the ages of 60 and 69, the mean
Making sure that the scales used by businesses in the United States are accurate is the responsibility of the National Institute for Standards and Technology (NIST)in Washington, D.C. Suppose that
One of the measurements used to determine the health of a person’s lungs is the amount of air a person can exhale under force in one second. This is called the forced expiratory volume in one
Are children heavier now than they were in the past? The National Health and Nutrition Examination Survey (NHANES) published in 2004 reported that the mean weight of six-year-old girls in the United
Data from the National Association of Realtors indicate that the mean price of a home in Denver, Colorado, in December 2016 was 366.5 thousand dollars. A random sample of 50 homes sold in 2017 had a
The College Board reports that in 2016 the mean score on the math SAT was 510 and the population standard deviation was σ = 103.A random sample of 20 students who took the test in 2017 had a mean
Environmental Protection Agency standards require that the amount of lead in drinking water be less than 15 micrograms per liter. Twelve samples of water from a particular source have the following
The mean GPA at a certain university is 2.80. Following are GPAs for a random sample of 16 business students from this university.a. Following is a boxplot of the data. Is it reasonable to assume
The age in years was recorded for a sample of books in a college library. The following display from a TI-84 Plus calculator presents the results of a hypothesis test regarding the mean age of books
The number of characters was determined for a sample of text messages sent by a certain student. The following display from a TI-84 Plus calculator presents the results of a hypothesis test regarding
A zoologist recorded the weight, in grams, for a sample of white-fronted Amazon parrots. The following MINITAB output presents the results of a hypothesis test regarding the mean weight of this
A sample of students at a certain college was drawn, and the age of each, in years, was determined. The following MINITAB output presents the results of a hypothesis test regarding the mean age of
A new method of teaching arithmetic to elementary school students was evaluated. The students who were taught by the new method were given a standardized test with a maximum score of 100 points. They
A new method of postoperative treatment was evaluated for patients undergoing a certain surgical procedure. Under the old method, the mean length of hospital stay was 6.3 days. The sample mean for
A math teacher has developed a new program to help high school students prepare for the math SAT. A sample of 100 students enroll in the program. They take a math SAT exam before the program starts
doctor has developed a new diet to help people lose weight. A random sample of 500 people went on the diet for six weeks. The mean number of pounds lost was x̄ = 0.5.Assume the standard deviation is
A test was made of the hypotheses H0: μ = 70 versus H1: μ ≠ 70.A report of the results stated:‘‘P < 0.05, so we reject H0 at the α = 0.05 level.’’ Is there any additional information
A test was made of the hypotheses H0: μ = 10 versus H1: μ > 10.A report of the results stated:‘‘The critical value was 1.645. Since z > 1.645, we reject H0 at the α = 0.05 level.’’ Is
Cindy computes a 95% confidence interval for μ and obtains (94.6, 98.3). Luis performs a test of the hypotheses H0: μ = 100 versus H1: μ ≠ 100 and obtains a P-value of 0.12. Explain why they
A sample of size n = 100 is used to test H0: μ = 20 versus H1: μ > 20.The value of μ will not have practical significance unless μ > 25.The population standard deviation is σ = 10.The value of
A simple random sample of 200 third graders in a large school district was chosen to participate in an after-school program to improve reading skills. After completing the program, the children were
In a preliminary study, a simple random sample of 100 computer chips was tested, and 17 of them were found to be defective. Now another sample will be drawn in order to construct a 95% confidence
A pollster is going to sample a number of voters in a large city and construct a 98% confidence interval for the proportion who support the incumbent candidate for mayor. Find a sample size so that
A pollster is planning to draw a simple random sample of 500 people in Colorado (population 5.5 million). He will then conduct a similar poll in Texas (population 27.9 million). He wants to have
A marketing firm in New York City (population 8.6 million) plans to draw a simple random sample of 1000 people to estimate the proportion who have heard about a new product. The firm then plans to
In a simple random sample of 15 seniors from a certain college, 8 of them had found jobs. Use the small-sample method to construct a 95% confidence interval for the proportion of seniors at that
If p̂ is the sample proportion and n is the sample size, then is the ____________________ .In Exercises 7 and 8, fill in each blank with the appropriate word or phrase. p(1 - p) n
To estimate the necessary sample size when no value of p̂ is available, we use p̂ = ______________ .In Exercises 7 and 8, fill in each blank with the appropriate word or phrase.
If we estimate the necessary sample size and no value for p̂ is available, the estimated sample size will be larger than if a value for p̂ were available.In Exercises 9 and 10, determine whether
The margin of error does not depend on the sample size.In Exercises 9 and 10, determine whether the statement is true or false. If the statement is false, rewrite it as a true statement.
x = 146, n = 762, confidence level 95%In Exercises 11–14, find the point estimate, the standard error, and the margin of error for the given confidence levels and values of x and n.
x = 46, n = 97, confidence level 99%In Exercises 11–14, find the point estimate, the standard error, and the margin of error for the given confidence levels and values of x and n.
x = 236, n = 474, confidence level 90%In Exercises 11–14, find the point estimate, the standard error, and the margin of error for the given confidence levels and values of x and n.
x = 29, n = 80, confidence level 92%In Exercises 11–14, find the point estimate, the standard error, and the margin of error for the given confidence levels and values of x and n.
x = 28, n = 64, confidence level 93%In Exercises 15–18, use the given data to construct a confidence interval of the requested level.
x = 52, n = 71, confidence level 97%In Exercises 15–18, use the given data to construct a confidence interval of the requested level.
x = 125, n = 317, confidence level 95%In Exercises 15–18, use the given data to construct a confidence interval of the requested level.
x = 178, n = 531, confidence level 90%In Exercises 15–18, use the given data to construct a confidence interval of the requested level.
Among 238 cell phone owners aged 18–24 surveyed by the Pew Research Center, 102 said their phone was an Android phone.a. Find a point estimate for the proportion of cell phone owners aged 18–24
According to the U.S. Census Bureau, 43% of men who worked at home were college graduates. In a sample of 500 women who worked at home, 162 were college graduates.a. Find a point estimate for the
Sleep apnea is a disorder in which there are pauses in breathing during sleep. People with this condition must wake up frequently to breathe. In a sample of 427 people aged 65 and over, 104 of them
An Internet service provider sampled 540 customers and found that 75 of them experienced an interruption in high-speed service during the previous month.a. Find a point estimate for the population
The General Social Survey asked 1294 people whether they performed any volunteer work during the past year. A total of 517 people said they did.a. Find a point estimate for the proportion of people
A college admissions officer sampled 120 entering freshmen and found that 42 of them scored more than 550 on the math SAT.a. Find a point estimate for the proportion of all entering freshmen at this
In the computer game League of Legends, some of the strikes are critical strikes, which do more damage.Assume that the probability of a critical strike is the same for every attack, and that attacks
In a sample of 42 water specimens taken from a construction site, 26 contained detectable levels of lead.a. Construct a 90% confidence interval for the proportion of water specimens that contain
A sociologist wants to construct a 95% confidence interval for the proportion of children aged 8–12 living in New York who own a cell phone.a. A survey by the National Consumers League estimated
An educator wants to construct a 98%confidence interval for the proportion of elementary schoolchildren in Colorado who are proficient in reading.a. The results of a recent statewide test suggested
A medical researcher wants to construct a 99% confidence interval for the proportion of knee replacement surgeries that result in complications.a. An article in the Journal of Bone and Joint Surgery
A pollster wants to construct a 95%confidence interval for the proportion of adults who believe that economic conditions are getting better.a. A Gallup poll estimates this proportion to be 0.34.
A sociologist sampled 200 people who work in computer-related jobs, and found that 42 of them have changed jobs in the past 6 months.a. Construct a 95% confidence interval for the proportion of those
A simple random sample of 300 voters was polled several months before a presidential election. One of the questions asked was: ‘‘Are you satisfied with the choice of candidates for
Eighteen concrete blocks were sampled and tested for crushing strength in order to estimate the proportion that were sufficiently strong for a certain application. Sixteen of the 18 blocks were
During an economic downturn, 20 companies were sampled and asked whether they were planning to increase their workforce. Only 3 of the 20 companies were planning to increase their workforce. Use the
A sample of voters in a certain city was asked whether they planned to vote for the incumbent mayor in the next election. The following display from a TI-84 Plus calculator presents a 99% confidence
A sample of employed people was asked whether they had changed jobs in the past two years.The following display from a TI-84 Plus calculator presents a 95% confidence interval for the population
A sample of drivers was asked whether they regularly use seat belts. The following MINITAB output presents a confidence interval for the population proportion who regularly use seat belts.a. Fill in
A football game starts with the toss of a coin to determine which team will get the ball first.Before the game, the referee tosses the coin a number of times and records the number of times the coin
The United States Senate consists of 100 senators. In January 2017, 21 of them were women. Explain why these data should not be used to construct a 95% confidence interval for the proportion of
At the end of a television documentary on the nature of government, viewers are invited to tweet an answer to the question, ‘‘Do you believe that women are more effective at governing than men
In a certain high school, 9 out of 15 tenth graders said they planned to go to college after graduating.Construct a 95% confidence interval for the proportion of tenth graders who plan to attend
Refer to Exercise 41.a. Which of the three confidence intervals is the narrowest?b. Does the small-sample method provide a good approximation to Wilson’s interval in this case?c. Explain why the
The small-sample method is a good approximation to Wilson’s method for all confidence levels commonly used in practice, but is best when zα∕2 is close to 2. Refer to Exercise 41.a. Use
Find the critical values for a 95% confidence interval using the chi-square distribution with 18 degrees of freedom.
Find the critical values for a 99% confidence interval using the chi-square distribution with 25 degrees of freedom.
Construct a 95% confidence interval for the population standard deviation σ if a sample of size 10 has standard deviation s = 6.
Construct a 99% confidence interval for the population standard deviation σ if a sample of size 23 has standard deviation s = 12.
To find a confidence interval for a standard deviation from a sample of size 15, we use a chi-square distribution with ____________ degrees of freedom.In Exercises 5 and 6, fill in each blank with
The method described for finding confidence intervals should be used only when the distribution of the population is almost exactly _________________ .In Exercises 5 and 6, fill in each blank with
When constructing a confidence interval for a standard deviation, we must find two critical values.In Exercises 7 and 8, determine whether the statement is true or false. If the statement is false,
If we have a confidence interval for a variance, we can obtain a confidence interval for the standard deviation by squaring the confidence bounds.In Exercises 7 and 8, determine whether the statement
Find the critical values for a 95% confidence interval using the chi-square distribution with 15 degrees of freedom.
Find the critical values for a 99% confidence interval using the chi-square distribution with 5 degrees of freedom.
Construct a 95% confidence interval for the population standard deviation σ if a sample of size 25 has standard deviation s = 15.
Scores on the math SAT are normally distributed.A sample of 20 SAT scores had standard deviation s = 87.a. Construct a 98% confidence interval for the population standard deviation σ.b. Someone says
Scores on an IQ test are normally distributed. A sample of 25 IQ scores had standard deviation s = 8.a. Construct a 95% confidence interval for the population standard deviation σ.b. The developer
Following are weights of 12 two-month-old baby girls. Assume that the population is normally distributed.a. Find the sample standard deviation s.b. Construct a 95% confidence interval for the
Boxes of cereal are labeled as containing 14 ounces. Following are the weights of a sample of 12 boxes.Assume that the population is normally distributed.a. Find the sample standard deviation s.b.
Six measurements were made of the mineral content (in percent) of spinach, with the following results.Assume that the population is normally distributed.a. Find the sample standard deviation s.b.
Following are interest rates (annual percentage rates) for a 30-year fixed rate mortgage from a sample of lenders in Macon, Georgia on a recent day. It is reasonable to assume that the population is
A sample of size 101 from a normal population has sample standard deviation s = 40.Use Table A.4 to find the exact critical values X2 0.025 and X2 0.975 for a 95% confidence interval, and construct a
Refer to Exercise 19.Use the normal approximation to estimate the critical values X2 0.025 and X2 0.975 for a 95% confidence interval, and construct a 95% confidence interval for σ.The chi-square
How close is the confidence interval based on the normal approximation constructed in Exercise 20 to the exact confidence interval constructed in Exercise 19?The chi-square distribution is skewed,
Refer to Exercise 19.Use the more accurate normal approximation to estimate the critical values X2 0.025 and X2 0.975 for a 95% confidence interval, and construct a 95% confidence interval for σ.A
How close is the confidence interval based on the more accurate normal approximation to the exact one?A more accurate normal approximation to X2 α is given bywhere zα is the z-score that has area
A simple random sample of size 15 has mean x̄ = 10.34 and standard deviation s = 3.48. The population is normally distributed. Construct a 95% confidence interval for the population standard
A simple random sample of size 80 has mean x̄ = 7.31. The population standard deviation is σ = 6.26. Construct a 99% confidence interval for the population mean.In Exercises 1–4, state which type
In a simple random sample of 100 children, 22 had reading skills above their grade level. Construct a 99% confidence interval for the proportion of children who have reading skills above their grade
A simple random sample of size 25 has mean x̄ = 17.4 and standard deviation s = 5.3. The population is approximately normally distributed. Construct a 95%confidence interval for the population
A simple random sample of size 18 has mean x̄ = 71.32 and standard deviation s = 15.78. The population is approximately normally distributed. Construct a 95% confidence interval for the population
In a simple random sample of 400 voters, 220 said that they were planning to vote for the incumbent mayor in the next election. Construct a 99% confidence interval for the proportion of voters who
A simple random sample of size 8 has mean x̄ = 3.21 and standard deviation s = 1.69. The population is normally distributed. Construct a 99% confidence interval for the population standard
A simple random sample of size 12 has mean x̄ = 3.37. The population standard deviation is σ = 1.62. The population is approximately normally distributed. Construct a 95%confidence interval for the
In a survey of 250 employed adults, 185 said that they had missed one or more days of work in the past six months.Construct a 95% confidence interval for the proportion of employed adults who missed
A simple random sample of size 17 has mean x̄ = 8.44 and standard deviation s = 5.38. The population is normally distributed. Construct a 95% confidence interval for the population standard
A simple random sample of size 120 has mean x̄ = 8.45. The population standard deviation is σ = 4.81. Construct a 99%confidence interval for the population mean.In Exercises 5–12, state which
A simple random sample of size 23 has mean x̄ = 1.48 and standard deviation s = 1.32. The population is approximately normally distributed. Construct a 99% confidence interval for the population
The weights of 52 randomly selected NFL football players are presented below. The sample mean is x̄ = 248.38 and the sample standard deviation is s = 46.68.Construct a 95% confidence interval for

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