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Statistics Informed Decisions Using Data 5th Edition Michael Sullivan III - Solutions

Researchers conducted a study to see the effect of specific lifestyle and dietary changes for preventing long-term weight gain. The study involved the consolidation of three cohorts from the Nurses' Health Study (NHS): (1) cohort of 121,701 female registered nurses, who enrolled in 1976; (2) the
What requirements must be satisfied in order to construct a confidence interval about a population proportion?
What requirements must be satisfied in order to construct a confidence interval about a population mean?
1. What is bootstrapping? Be sure to include a discussion of the general bootstrap algorithm. 2. If we wish to obtain a 95% confidence interval of a parameter using the bootstrap percentile method, we determine the ________ percentile and the _________ percentile of the resampled distribution?
The following data represent the selling price (in thousands of dollars) of oceanfront condominiums in Daytona Beach Shores, Florida.(a) Draw a boxplot of the data. Explain why a t-interval should not be constructed.(b) Obtain 1000 bootstrap samples and determine the mean of each sample. Draw a
The following data represent the annual 2015 salary (in thousands of dollars) of a random sample of professional baseball players.(a) Draw a boxplot of the data. Explain why a t-interval should not be constructed.(b) Obtain 1000 bootstrap samples and determine the mean of each sample. Draw a
To estimate proportions using bootstrapping methods, report successes as 1 and failures as 0. Then follow the same procedures that we used to estimate a mean using bootstrapping. A random sample of 85 adult Americans was asked, "Have you ever ended a budding relationship because a kiss did not go
To estimate proportions using bootstrapping methods, report successes as 1 and failures as 0. Then follow the same procedures that we used to estimate a mean using bootstrapping. Suppose a random sample of 25 50- to 64-year-old Americans were asked if they feel younger than their actual age. In the
Suppose the following data represent the heights (in inches) of a random sample of males: 68, 72, 73, 70, 75, 71. Which of the following could be a possible bootstrap sample? (a) 68, 72, 72, 68, 70, 71 (b) 75, 72, 73, 73, 68 (c) 70, 71, 68, 73, 73, 71, 68 (d) 72, 73, 75, 71, 73, 63 (e) 68, 72, 73,
Suppose the following data represent the amount of time (in hours) a random sample of students enrolled in College Algebra spent working on a homework assignment: 3.2, 4.1, 1.2, 0.6, and 2.5. Which of the following could be a possible bootstrap sample? (a) 4.1, 1.2, 1.2, 2.5 (b) 2.5, 0.6, 3.2, 0.6,
Suppose the following data represent the heights (in inches) of a random sample of males: 68, 72, 73, 70, 75, 71. Below are three bootstraps samples. For each bootstrap sample, determine the bootstrap sample mean.Bootstrap Sample 1: 68, 72, 68, 73, 72, 75Bootstrap Sample 2: 71, 72, 73, 72, 72,
Suppose the following data represent the amount of time (in hours) a random sample of students enrolled in College Algebra spent working on a homework assignment: 3.2, 4.1, 1.2, 0.6, and 2.5. Below are three bootstraps samples. For each bootstrap sample, determine the bootstrap sample
The following data represent the pH of rain for a random sample of 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 outliers. In Problem 31 from Section 9.2, we found a
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). In Problem 33 from Section 9.2, we obtained a 95% confidence interval for the mean repair cost of a low-impact collision
Find the critical t-value for constructing a confidence interval for a population mean at the given level of confidence for the given sample size, n.(a) 99% confidence; n = 18(b) 90% confidence; n = 27
In a survey of 35 adult Americans, it was found that the mean age (in years) that people would like to live to is 87.9 with a standard deviation of 15.5. An analysis of the raw data indicates the distribution is skewed left.(a) Explain why a large sample size is necessary to construct a confidence
The General Social Survey asked: "How many e-mails do you send in a day?" The results of 928 respondents indicate that the mean number of e-mails sent in a day is 10.4, with a standard deviation of 28.5.(a) Given the fact that 1 standard deviation to the left of the mean results in a negative
The diameter of the Douglas fir tree is measured at a height of 1.37 meters. The following data represent the diameter in centimeters of a random sample of 12 Douglas firs in the western Washington Cascades.(a) Obtain a point estimate for the mean and standard deviation diameter of a Douglas fir
Use the data from Problem 15 on the diameter of Douglas fir trees.(a) Construct and interpret a 95% confidence interval for the mean diameter of a Douglas fir tree using a bootstrap sample with 1000 resamples. Compare the bootstrap confidence interval to the t-interval found in Problem 15(c).(b)
Find the critical values (21-α/2 and (2α/2 required to construct a confidence interval for s for the given level of confidence and sample size.(a) 95% confidence; n = 22(b) 99% confidence; n = 12
Many of the examples and exercises in the text have dealt with IQ scores. We now know that IQ scores based on the Stanford-Binet IQ test are approximately normally distributed with a mean of 100 and standard deviation 15. If you were to obtain 100 different simple random samples of size 20 from the
For what proportion of samples will a 90% confidence interval for a population mean not capture the true population mean?
In 2011, 90,000 fires in the United States were started by a lighted tobacco product. The dollar value of the property lost in these fires is staggering. In that same year, fires caused by dropped or discarded cigarettes resulted in 540 deaths. Twenty-five percent of the victims of cigarette
For students who first enrolled in twoyear public institutions in fall 2007, the proportion who earned a bachelor's degree within six years was 0.399. The president of Joliet Junior College believes that the proportion of students who enroll in her institution have a higher completion
Pizza Historically, the time to order and deliver a pizza at Jimbo's pizza was 48 minutes. Jim, the owner, implements a new system for ordering and delivering pizzas that he believes will reduce the time required to get a pizza to his customers.Determine the null and alternative hypotheses, (b)
Single-Family Home Price According to the National Association of Home Builders, the mean price of an existing single-family home in 2013 was $245,700. A real estate broker believes that existing home prices in her neighborhood are lower.Determine the null and alternative hypotheses, (b) explain
Cell Phone Service According to the CTIA-The Wireless Association, the mean monthly revenue per cell phone was $48.79 in 2014. A researcher suspects the mean monthly revenue per cell phone is different today.Determine the null and alternative hypotheses, (b) explain what it would mean to make a
In 2014, the standard deviation of SAT score on the Critical Reading Test for all students taking the exam was 112. A teacher believes that, due to changes to high school curricula, the standard deviation of SAT math scores has decreased. Determine the null and alternative hypotheses, (b) explain
A can of soda is labeled as containing 12 fluid ounces. The quality control manager wants to verify that the filling machine is neither over-filling nor under-filling the cans. (a) Determine the null and alternative hypotheses that would be used to determine if the filling machine is calibrated
E-Cigs According to the Centers for Disease Control and Prevention, 2.8% of high school students currently use electronic cigarettes. A high school counselor is concerned the use of e-cigs at her school is higher. (a)Determine the null and alternative hypotheses. (b)If the sample data indicate
Retirement Savings Designed by Bill Bengen, the 4 percent rule says that a retiree may withdraw 4% of savings during the first year of retirement, and then each year after that withdraw the same amount plus an adjustment for inflation. Under this rule, your retirement savings should be expected to
The website pundittracker.com keeps track of predictions made by individuals in finance, politics, sports, and entertainment. Jim Cramer is a famous TV financial personality and author. Pundittracker monitored 678 of his stock predictions (such as a recommendation to buy the stock) and found that
In his book, "The Signal and the Noise," Nate Silver analyzed 733 predictions made by experts regarding political events. Of the 733 predictions, 338 were mostly true.(a)Determine the sample proportion of political predictions that were mostly true.(b)Suppose that we want to know whether the
According to the National Highway and Traffic Safety Administration, the proportion of fatal traffic accidents in the United States in which the driver had a positive blood alcohol concentration (BAC) is 0.36. Suppose a random sample of 105 traffic fatalities in the state of Hawaii results in 51
A headline read, "More Than Half of Americans Say Federal Taxes Too High." The headline was based on a random sample of 1026 adult Americans in which 534 stated the amount of federal tax they have to pay is too high. Is this an accurate headline?State the conclusion based on the results of the test.
The Sullivan Statistics Survey II asked, "Do you believe there is an income inequality discrepancy between males and females when each has the same experience and education?" Go to www.pearsonhighered.com/sullivanstats to obtain the data file SullivanStatsSurveyII using the file format of your
Parapsychology (psi) is a field of study that deals with clairvoyance or precognition. Psi made its way back into the news when a professional, refereed journal published an article by Cornell psychologist Daryl Bem, in which he claimed to demonstrate that psi is a real phenomenon. In the article
Calcium is essential to tree growth. In 1990, the concentration of calcium in precipitation in Chautauqua, New York, was 0.11 milligram per liter (mg/L). A random sample of 10 precipitation dates in 2014 results in the following data:A normal probability plot suggests the data could come from a
The volume of a stock is the number of shares traded for a given day. In 2011, Starbucks stock had a mean daily volume of 7.52 million shares according to Yahoo!Finance. A random sample of 40 trading days in 2014 was obtained and the volume of shares traded on those days was recorded. Go to
(a) Draw a histogram of the data. Describe the shape of the distribution.(b) Draw a boxplot of the data. Are there any outliers?(c) Based on the shape of the histogram and boxplot, explain why a large sample size is necessary to perform inference on the mean using the normal model.(d) According to
It is well-documented that watching TV, working on a computer, or any other activity involving artificial light can be harmful to sleep patterns. Researchers wanted to determine if the artificial light from e-Readers also disrupted sleep. In the study, 12 young adults were given either an iPad or
A machine fills bottles with 64 fluid ounces of liquid. The quality-control manager determines that the fill levels are normally distributed with a mean of 64 ounces and a standard deviation of 0.42 ounce. He has an engineer recalibrate the machine in an attempt to lower the standard deviation.
The piston diameter of a certain hand pump is 0.5 inch. The quality-control manager determines that the diameters are normally distributed, with a mean of 0.5 inch and a standard deviation of 0.004 inch. The machine that controls the piston diameter is recalibrated in an attempt to lower the
The manufacturer of processed deli meats reports that the standard deviation of the number ofcarbohydrates in its smoked turkey breast is 0.5 gram per 2-ounce serving. A dietitian does not believe the manufacturer and randomly selects eighteen 2-ounce servings of the smoked turkey breast and
In Problem 21 from Section 10.3, we considered the mean waiting time at the drive-through of a fast-food restaurant. The manager is also worried about the variability in wait times. Prior to the new drive-through system, the standard deviation of wait time was 18.0 seconds. Use the data in the
In Problem 24 from Section 10.3, we considered whether a filling machine was calibrated correctly. Another aspect of the calibration is the variability in the amount of juice in the bottle. Suppose the machine is calibrated so that it fills the bottles with a standard deviation of 0.04 ounce. Do
Sports announcers often say, "I wonder which player will show up to play today." This is the announcer's way of saying that the player's performance varies dramatically from game to game. Suppose that the standard deviation of the number of points scored by shooting guards in the NBA is 8.3. A
One aspect of queuing theory is to consider waiting time in lines. A fast-food chain is trying to determine whether it should switch from having four cash registers with four separate lines to four cash registers with a single line. It has been determined that the mean wait-time in both lines is
Data obtained from the National Center for Health Statistics show that men between the ages of 20 and 29 have a mean height of 69.3 inches, with a standard deviation of 2.9 inches. A baseball analyst wonders whether the standard deviation of heights of major-league baseball players is less than 2.9
NCAA rules require the circumference of a softball to be 12 { 0.125 inches. Suppose that the NCAA also requires that the standard deviation of the softball circumferences not exceed 0.05 inch. A representative from the NCAA believes the manufacturer does not meet this requirement. She collects a
To test H0: σ = 35 versus H1: σ ˃ 35, a random sample of size n = 15 is obtained from a population that is known to be normally distributed. (a) If the sample standard deviation is determined to be s = 37.4, compute the test statistic. (b) If the researcher decides to test this hypothesis at
To test H0: σ = 1.8 versus H1: σ 7 1.8, a random sample of size n = 18 is obtained from a population that is known to be normally distributed. (a) If the sample standard deviation is determined to be s = 2.4, compute the test statistic. (b) If the researcher decides to test this hypothesis at the
To test H0: σ = 0.35 versus H1: σ 6 0.35, a random sample of size n = 41 is obtained from a population that is known to be normally distributed. (a) If the sample standard deviation is determined to be s = 0.23, compute the test statistic. (b) If the researcher decides to test this hypothesis at
To test H0: σ = 4.3 versus H1: σ ≠ 4.3, a random sample of size n = 12 is obtained from a population that is known to be normally distributed.(a) If the sample standard deviation is determined to be s = 4.8, compute the test statistic.(b)If the researcher decides to test this hypothesis at the
To test H0: σ = 1.2 versus H1: σ ≠ 1.2, a random sample of size n = 22 is obtained from a population that is known to be normally distributed.(a) If the sample standard deviation is determined to be s = 0.8, compute the test statistic.(b) If the researcher decides to test this hypothesis at the
One measure of the risk of a mutual fund is the standard deviation of its rate of return. Suppose a mutual fund qualifies as having moderate risk if the standard deviation of its monthly rate of return is less than 4%. A mutual-fund manager claims that his fund has moderate risk. A mutual-fund
A manufacturer of high-strength, lowalloy steel beams requires that the standard deviation of yield strength not exceed 7000 pounds per square inch (psi). The quality-control manager selected a sample of 20 steel beams and measured their yield strength. The standard deviation of the sample was 7500
A pharmaceutical company manufactures a 200-milligram (mg) pain reliever. Company specifications require that the standard deviation of the amount of the active ingredient must not exceed 5 mg. The quality-control manager selects a random sample of 30 tablets from a certain batch and finds that the
Pass rates for Intermediate Algebra at a community college are 52.6%. In an effort to improve pass rates in the course, faculty of a community college develop a mastery based learning model where course content is delivered in a lab through a computer program. The instructor serves as a learning
According to the Federal Reserve Bank of Boston, among individuals who had credit cards in 2014, the mean number of cards was 3.5. Treat the individuals who have credit cards in the SullivanStatsSurveyI as a random sample of credit card holders. Go to www.pearsonhighered.com/ Sullivan stats to
The Environmental Protection Agency (EPA) states that a 2013 Kia Optima should get 28 miles per gallon, on average. The website www.fueleconomy.gov allows users to report the miles per gallon that they get on their vehicle. Treat the following data as a random sample of ten 2013 Kia Optima owners.
According to the National Sleep Foundation, children between the ages of 6 and 11 years should get 10 hours of sleep each night. In a survey of 56 parents of 6 to 11 year olds, it was found that the mean number of hours the children slept was 8.9 with a standard deviation of 3.2. Does the sample
Student loan debt has reached record levels in the United States. In a random sample of 100 individuals who have student loan debt, it was found the mean debt was $23,979 with a standard deviation of $31,400. Data based on results from the Federal Reserve Bank of New York. (a) What do you believe
A survey from the Gallup organization asked, "What do you think is the ideal number of children for a family to have?" Go to www.pearsonhighered.com/sullivanstats to obtain the data file 10_5_21 using the file format of your choice for the version of the text you are using to get the survey
Suppose you wish to determine if the mean IQ of students on your campus is different from the mean IQ in the general population, 100. To conduct this study, you obtain a simple random sample of 50 students on your campus, administer an IQ test, and record the results. The mean IQ of the sample of
A psychologist obtains a random sample of 20 mothers in the first trimester of their pregnancy. The mothers are asked to play Mozart in the house at least 30 minutes eachday until they give birth. After 5 years, the child is administered an IQ test. We know that IQs are normally distributed with a
ACT, a college entrance exam used for admission, looked at historical records and established 21 as the minimum score on the ACT reading portion of the exam for a student to be considered prepared for social science in college. (Note: "Being prepared" means there is a 75% probability of
In August 2002, 47% of parents who had children in grades K-12 were satisfied with the quality of education the students receive. A recent Gallup poll found that 437 of 1013 parents of children in grades K-12 were satisfied with the quality of education the students receive. Does this suggest the
In December 2001, 38% of adults with children under the age of 18 reported that their family ate dinner together seven nights a week. In a recent poll, 403 of 1122 adults with children under the age of 18 reported that their family ate dinner together seven nights a week. Has the proportionof
In 1994, 52% of parents of children in high school felt it was a serious problem that high school students were not being taught enough math and science. A recent survey found that 256 of 800 parents of children in high school felt it was a serious problem that high school students were not being
According to menstuff.org, 22% of married men have "strayed" at least once during their married lives. A survey of 500 married men indicated that 122 have strayed at least once during their married life. Does this survey result contradict the results of menstuff.org? (a) What does it mean to make a
Effect of A Redo Problem 3(b) with α = 0.01. What effect does lowering the level of significance have on the power of the test? Why does this make sense?
Redo Problem 4(b) with α = 0.01. What effect does lowering the level of significance have on the power of the test? Why does this make sense?
Draw a power curve for the scenario in Problem 3 by finding the power of the test for p = 0.2, 0.22, 0.24, 0.26, 0.28 [done in part (b)], and 0.29.
Draw a power curve for the scenario in Problem 4 by finding the power of the test for p = 0.41, 0.42, 0.44 [done in part (b)], 0.46, 0.48, and 0.50.
To test H0: m = 50 versus H1: m 6 50, a simple random sample of size n = 24 is obtained from a population that is known to be normally distributed, and the sample standard deviation is found to be 6.(a) A researcher decides to test the hypothesis at the a = 0.05 level of significance. Determine the
Explain the term power of the test.
What happens to the power of the test as the true value of the parameter gets closer to the value of the parameter stated in the null hypothesis? Why is this result reasonable?
To test H0: p = 0.30 versus H1: p ˂ 0.30, a simple random sample of n = 300 individuals is obtained and x = 86 successes are observed.(a) What does it mean to make a Type II error for this test?(b) If the researcher decides to test this hypothesis at the α = 0.05 level of significance, compute
To test H0: p = 0.65 versus H1: p 7 0.65, a simple random sample of n = 100 individuals is obtained and x = 69 successes are observed.(a) What does it mean to make a Type II error for this test?(b) If the researcher decides to test this hypothesis at the α = 0.01 level of significance, compute the
To test H0: p = 0.75 versus H1: p 6 < 0.75, a simple random sample of n = 400 individuals is obtained and x = 280 successes are observed.(a) What does it mean to make a Type II error for this test?(b) If the researcher decides to test this hypothesis at the α = 0.01 level of significance,
To test H0: p = 0.45 versus H1: p ≠ 0.45, a simple random sample of n = 500 individuals is obtained and x = 245 successes are observed.(a) What does it mean to make a Type II error for this test?(b) If the researcher decides to test this hypothesis at the α = 0.1 level of significance, compute
To test H0: p = 0.25 versus H1: p ≠ 0.25, a simple random sample of n = 350 individuals is obtained and x = 74 successes are observed.(a) What does it mean to make a Type II error for this test?(b) If the researcher decides to test this hypothesis at the α = 0.05 level of significance, compute
In April 2009, the Gallup organization surveyed 676 adults aged 18 and older and foundthat 352 believed they would not have enough money to live comfortably in retirement. The folks at Gallup want to know if this represents sufficient evidence to conclude a majority (morethan 50%) of adults in the
To test H0: σ = 15.7 versus H1: σ ˃ 15.7, a simple random sample of size n = 25 is obtained from a population that is known to be normally distributed.(a) If the sample standard deviation is determined to be s = 16.5, compute the test statistic.(b) Test this hypothesis at the α = 0.1 level of
A linear rotary bearing is designed so that the distance between the retaining rings is 0.875 inch. The quality-control manager suspects that the manufacturing process needs to be recalibrated because the mean distance between the retaining rings is greater than 0.875 inch. In a random sample of 36
(a) Explain what it would mean to make a Type II error for this test.(b) Determine the probability of making a Type II error if the true population proportion of pregnant women who nap is 0.53. What is the power of the test?
An obstetrician maintains that preterm babies (gestation period less than 37 weeks) have a higher variability in birth weight than do full-term babies (gestation period 37 to 41 weeks). According to the National Vital Statistics Report, the birth weights of full-term babies are normally
Throughout the country, the proportion of first time, first-year community college students who return for their second year of studies is 0.52 according to the Community College Survey of Student Engagement. Suppose a community college institutes new policies geared toward increasing student
In 1995, 40% of adolescents stated they prayed daily. A researcher wants to know whether this percentage has risen since then. He surveys 40 adolescents and finds that 18 pray on a daily basis. Is this evidence that the proportion of adolescents who pray daily has increased at the α = 0.05 level
A large university has a college algebra enrollment of 5000 students each semester. Because of space limitations, the university decides to offer its college algebra courses in a self-study format in which students learn independently, but have access to tutors and other help in a lab setting.
To test H0: σ = 5.2 versus H1: σ ≠ 5.2, a simple random sample of size n = 18 is obtained from a population that is known to be normally distributed.(a) If the sample standard deviation is determined to be s = 4.9, compute the test statistic.(b) Test this hypothesis at the α = 0.05 level of
Approximately eight miles north of Salisbury, Wiltshire, England, stands a large prehistoric circular stone monument surrounded by an earthwork, called Stonehenge. The monument consists of an outer ring of sarsen stones, surrounding two inner circles of bluestones. The entire structure is
In randomized, double-blind clinical trials of Prevnar, infants were randomly divided into two groups. Subjects in group 1 received Prevnar, while subjects in group 2 received a control vaccine. After the second dose, 137 of 452 subjects in the experimental group (group 1) experienced drowsiness as
Researchers at Harris Interactive wondered if there was a difference between males and females in regard to some common annoyances. They asked a random sample of males and females, the following question: "Are you annoyed by people who repeatedly check their mobile phones while having an in-person
Researchers at Harris Interactive wondered if there was a difference between males and females in regard to whether they typically buy name-brand or store-brand products. They asked a random sample of males and females the following question: "For each of the following types of products, please
In clinical trials of the allergy medicine Clarinex (5 mg), 3307 allergy sufferers were randomly assigned to either a Clarinex group or a placebo group. It was reported that 50 out of 1655 individuals in the Clarinex group and 31 out of 1652 individuals in the placebo group experienced dry mouth as
A sociologist wishes to compare the annual salaries of married couples in which both spouses work and determines each spouse's annual salary. Determine whether the sampling is dependent or independent. Indicate whether the response variable is qualitative or quantitative.
Psychologists asked students to read two sentences about hypothetical politicians. Ninety-eight students read, "Last year, Mark was having an affair with his assistant and was taking hush money from a prominent constituent." Let's call this sentence A. Ninety-eight other students read, "Last year,
In June 2014, the Gallup organization surveyed 1134 American adults and found that 298 had confidence in public schools. In June 2013, the Gallup organization had surveyed 1134 American adults and found that 360 had confidence in public schools. Suppose that a newspaper article has a headline that

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