A machine at K&A Tube & Manufacturing Company produces a certain copper tubing component in a refrigeration unit. The tubing components produced by the manufacturer have a mean diameter of 0.75 inch with a standard deviation of 0.004 inch. The quality-control inspector takes a random sample of 30 components once each week and calculates the mean diameter of these components. If the mean is either less than 0.748 inch or greater than 0.752 inch, the inspector concludes that the machine needs an adjustment. (a) Describe the sampling distribution of /, the sample mean diameter, for a random sample of 30 such components. (b) What is the probability that, based on a random sample of 30 such components, the inspector will conclude that the machine needs an adjustment when, in fact, the machine is correctly calibrated?
> The U.S. Golf Association (USGA) requires that golf balls have a diameter that is 1.68 inches. To determine if Maxfli XS golf balls conform to USGA standards, a random sample of Maxfli XS golf balls was selected. Their diameters are shown in the table. (
> 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 2018, answer the following questions: (a) What is the pro
> Carl Reinhold August Wunderlich said that the mean temperature of humans is 98.6°F. Researchers Philip Mackowiak, Steven Wasserman, and Myron Levine [JAMA, Sept. 23–30 1992; 268(12):1578–80] thought that the mean temperature of humans is less than 98.6°F
> The following represent the results of a survey in which individuals were asked to disclose what they perceive to be the ideal number of children. (a) What is the probability an individual believes the ideal number of children is 2? (b) What is the proba
> 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 grea
> The following probability model shows the distribution of the most-popular-selling Girl Scout Cookies®. (a) Verify that this is a probability model. (b) If a girl scout is selling cookies to people who randomly enter a shopping mall, what is the probabil
> Does a platelet-rich plasma (PRP) injection into the scalp promote hair growth? Researchers identified 30 female patients with female pattern hair loss. The patients ranged in age from 20 to 45 years. For each patient, two areas with hair loss were ident
> The proportion of patients who visit the emergency room (ER) and die within the year is 0.05. Source: SuperFreakonomics. Suppose a hospital administrator is concerned that his ER has a higher proportion of patients who die within the year. In a random sa
> Which among the following numbers could be the (c) If a girl scout is selling cookies to people who randomly probability of an event? /
> According to creditcard.com, the mean outstanding credit-card debt of college undergraduates was $3173 in 2010. A researcher believes that this amount has decreased since then.
> What would you say about a set of quantitative bivariate data whose linear correlation coefficient is -1? What would a scatter diagram of the data look like?
> A simple random sample of size n is drawn from a population that is known to be normally distributed. The sample mean, /, is determined to be 104.3 and the sample standard deviation, s, is determined to be 15.9. (a) Construct the 90% confidence interval
> What does it mean if a linear correlation coefficient is close to zero? Draw two scatter diagrams for which the linear correlation coefficient is close to zero.
> A simple random sample of size n is drawn from a population. The sample mean, /, is 54.8 and the sample standard deviation is 10.5. (a) Construct the 90% confidence interval for the population mean if the sample size, n, is 30. (b) Construct the 90% conf
> If the slope of a least-squares regression line is negative, what could be said about the correlation between the explanatory and response variable?
> State the properties of Student’s t-distribution.
> Which is larger, the area under the t-distribution with 10 degrees of freedom to the right of t = 2.32 or the area under the standard normal distribution to the right of z = 2.32? Why?
> Researchers wanted to determine whether the stomach shrinks as a result of dieting. To do this, they randomly divided 23 obese patients into two groups. The 14 individuals in the experimental group were placed on a diet that allowed them to consume 2508
> Consider the following contingency table, which relates the number of applicants accepted to a college and gender. (a) Construct a conditional distribution of acceptance status by gender. (b) What proportion of males was accepted? What proportion of fema
> The area under the t-distribution with 18 degrees of freedom to the right of t = 1.56 is 0.0681. What is the area under the t-distribution with 18 degrees of freedom to the left of t = -1.56? Why?
> What is the relationship between education and belief in Heaven? The following data represent the highest level of education and belief in Heaven for a random sample of adult Americans. (a) Construct a relative frequency marginal distribution. (b) What p
> For what proportion of samples will a 90% confidence interval for a population mean not capture the true population mean?
> A researcher collects data regarding the percent of all births to unmarried women and the number of violent crimes for the 50 states and Washington, DC. The scatter diagram along with the least-squares regression line obtained from Minitab is shown on th
> What does the 95% represent in a 95% confidence interval?
> Use the results from Problems 1 and 2 to compute and interpret R2.
> 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 differ
> Use the data from Problem 1. (a) Find the least-squares regression line treating temperature as the explanatory variable and chirps per second as the response variable. (b) Interpret the slope and y-intercept, if appropriate. (c) Predict the chirps per s
> In a random sample of 678 adult males 20 to 34 years of age, it was determined that 58 of them have hypertension (high blood pressure). Source: The Centers for Disease Control. (a) Obtain a point estimate for the proportion of adult males 20 to 34 years
> Researchers wanted to evaluate whether ginkgo, an over-the-counter herb marketed as enhancing memory, improves memory in elderly adults as measured by objective tests. To do this, they recruited 98 men and 132 women older than 60 years and in good health
> Crickets make a chirping noise by sliding their wings rapidly over each other. Perhaps you have noticed that the number of chirps seems to increase with the temperature. The following data list the temperature (in degrees Fahrenheit) and the number of ch
> 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. Source: L. Winter. “Live Tree and Tree-Ring Re
> The following data represent the weights (in grams) of 50 randomly selected quarters. Determine and interpret the quartiles. Does the data set contain any outliers?
> A random sample of 60 married couples who have been married 7 years was asked the number of children they have. The results of the survey are as follows: Note: / = 2.27, s = 1.22. (a) What is the shape of the distribution of the sample mean? Why? (b) Com
> An engineer is studying bearing failures for two different materials in aircraft gas turbine engines. The following data are failure times (in millions of cycles) for samples of the two material types. (a) Determine the sample mean failure time for each
> Researchers conducted an experiment to determine the effectiveness of a commercial caffeinated carbohydrate–electrolyte sports drink compared with a placebo. Sixteen highly trained cyclists each completed two trials of prolonged cycling in a warm environ
> Yolanda wishes to develop a new type of meatloaf to sell at her restaurant. She decides to combine 2 pounds of ground sirloin (cost $2.70 per pound), 1 pound of ground turkey (cost $1.30 per pound), and 1/2 pound of ground pork (cost $1.80 per pound). Wh
> 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 th
> The following data represent the length of time (in minutes) between eruptions of Old Faithful in Yellowstone National Park. (a) Approximate the mean length of time between eruptions. (b) Approximate the standard deviation length of time between eruption
> 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 sampl
> Researchers wanted to test the effectiveness of a new cognitive behavioral therapy (CBT) compared with both an older behavioral treatment and a placebo therapy for treating insomnia. They identified 75 adults with insomnia. Patients were randomly assigne
> In a random sample of 250 toner cartridges, the mean number of pages a toner cartridge can print is 4302 and the standard deviation is 340. (a) Suppose a histogram of the data indicates that the sample data follow a bell-shaped distribution. According to
> 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
> (a) Determine the standard deviation of the homework data from Problem 1. (b) By hand, determine and interpret the interquartile range of the homework data from Problem 1. (c) Which of these two measures of dispersion is resistant? Why?
> 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 selected adults 25 years of age or older and finds that 60 o
> Determine the range of the homework data from Problem 1.
> A Gallup survey indicated that 72% of 18- to 29-year-olds, if given a choice, would prefer to start their own business rather than work for someone else. A random sample of 600 18- to 29-year-olds is obtained today. (a) Is the variable start own business
> The Federal Bureau of Investigation classifies various larcenies. The data below represent the type of larcenies based on a random sample of 15 larcenies. What is the mode type of larceny?
> Based on data obtained from AC Nielsen, the mean number of televisions in a household in the United States is 2.24. Assume that the population standard deviation number of television sets in the United States is 1.38. (a) Do you believe the shape of the
> Explain how the standard deviation measures dispersion. In your explanation, include a discussion of deviation about the mean.
> The principle of ideomotor action suggests that the act of thinking about a behavior increases the tendency to engage in that behavior. This is sometimes referred to as “priming.” In one such study, 30 male and female undergraduate students were randomly
> Answer the following based on the histograms shown in the next column. (a) Which measure of central tendency would you recommend reporting for the data whose histogram is shown in Figure I? Why? (b) Which one has more dispersion? Explain.
> The total energy need during pregnancy is normally distributed, with mean = 2600 kcal/day and standard deviation= 50 kcal/day. Source: American Dietetic Association. (a) Is total energy need during pregnancy qualitative or quantitative? (b) What is
> The distribution of income tends to be skewed to the right. Suppose you are running for a congressional seat and wish to portray that the average income in your district is low. Which measure of central tendency, the mean or the median, would you report?
> What are the mean and standard deviation of the sampling distribution of /? What are the mean and standard deviation of the sampling distribution of /?
> According to the National Center for Health Statistics, a 10-year-old male whose height is 53.5 inches has a height that is at the 15th percentile. Explain what this means.
> Under what conditions is the sampling distribution of / approximately normal?
> Armando is filling out a college application that requires he supply either his SAT math score or his ACT math score. Armando scored 610 on the SAT math and 27 on the ACT math. Which score should Armando report, given that the mean SAT math score is 515
> Under what conditions is the sampling distribution of / normal?
> The following data represent the amount of time (in minutes) a random sample of eight students enrolled in Sullivan’s Intermediate Algebra course spent on the homework from Section 4.5, Factoring Polynomials. (a) Determine the mean amount of time spent d
> Suppose, during the course of a typical season, a batter has 500 at-bats. This means the player has the opportunity to get a hit 500 times during the course of a season. Further, suppose a batter is a career 0.280 hitter (he averages 280 hits every 1000
> To help assess student learning in her developmental math courses, a mathematics professor at a community college implemented pre- and posttests for her students. A knowledge-gained score was obtained by taking the difference of the two test scores. (a)
> The following is a USA Today-type graph. Do you think the graph is misleading? Why? If you think it is misleading, improve the graph?
> In your own words, explain what a sampling distribution is.
> The data in the next column shows birth rate and per capita income (in thousands of 2012 dollars) from 2005 through 2017. Draw a time-series plot for both birth rate and per capita income. Comment on any trends.
> = 70, = 10, P(65 < X < 85)
> = 30, = 5, P(X ≤ 23)
> The following data represent the time (in minutes) students spent working their Section 1.1 homework from Sullivan’s College Algebra course (based on time logged into MyLabMath). Draw a stem-and-leaf diagram of the data and comment on the shape of the di
> = 50, = 6, PX 55
> Dr. Paul Oswiecmiski randomly selects 40 of his 20- to 29-year-old patients and obtains the following data regarding their serum HDL cholesterol: (a) Construct a frequency distribution. (b) Construct a relative frequency distribution. (c) Construct a fre
> Find the value of z0.20.
> The following data represent the number of cars that arrived at a McDonald’s drive-through between 11:50 A.M. and 12:00 noon each Wednesday for the past 50 weeks: (a) Construct a frequency distribution of the data. (b) Construct a relative frequency dist
> An ad for Crest Whitestrips Premium claims that the strips will whiten teeth in 7 days and the results will last for 12 months. A researcher who wishes to test this claim studies 20 sets of identical twins. Within each set of twins, one is randomly selec
> Length (in minutes) of a country song
> Find the z-scores that separate the middle 92% of the data from the area in the tails of the standard normal distribution.
> Interested in knowing the educational background of its customers the Metra Train Company contracted a marketing firm to conduct a survey asking 50 randomly selected commuters at the train station to disclose their educational attainment. The results sho
> Find the z-score such that the area to the right of the z-score is 0.483.
> A random sample of 1005 adult Americans was asked, “How would you prefer to pay for new road construction?” Results of the survey are below. (a) Construct a relative frequency distribution. (b) What percent of the respondents indicated they would like to
> The area between z = -0.34 and z = 1.03.
> The graph shows the ratings on Yelp for Hot Doug’s Restaurant. (a) Which was the most popular rating for Hot Doug’s? (b) How many ratings were posted on Hot Doug’s? (c) How many more 5 Star ratings are there than 4 Star ratings? (d) What percentage of ra
> Explain how to use a normal probability plot to assess normality.
> Explain the difference between a lurking variable and a confounding variable.
> The area to the left of z = -1.04.
> Researchers Katherine Tucker and associates wanted to determine whether consumption of cola is associated with lower bone mineral density. They looked at 1125 men and 1413 women in the Framingham Osteoporosis Study, which is a cohort that began in 1971.
> A pharmaceutical company has developed an experimental drug meant to relieve symptoms associated with the common cold. The company identifies 300 adult males 25 to 29 years old who have a common cold and randomly divides them into two groups. Group 1 is
> List the properties of the normal density curve.
> Nucryst Pharmaceuticals, Inc., announced the results of its first human trial of NPI 32101, a topical form of its skin ointment. A total of 225 patients diagnosed with skin irritations were randomly divided into three groups as part of a double-blind, pl
> A continuous random variable X is uniformly distributed with / (a) Draw a graph of the uniform density function. (b) What is / (c) What is /
> Does the shape of a glass play a role in determining the amount of time it takes to finish the drink? Researchers identified 159 male and female self- professed social drinkers. One week the subjects were given a 12 ounce beer with either a straight g
> According to a USA Today “Snapshot,” 20% of adults surveyed do their most creative thinking while driving. You conduct a survey of 250 adults and find that 30 do their most creative thinking while driving. (a) Compute the probability that, in a random sa
> Each of the following surveys has bias. Identify the type of bias. (a) A television survey that gives 900 phone numbers for viewers to call with their vote. Each call costs $2.00. (b) An employer distributes a survey to her 450 employees asking them how
> In 1798, Henry Cavendish obtained 27 measurements of the density of Earth, using a torsion balance. The following data represent his estimates, given as a multiple of the density of water. Is it reasonable to conclude that the sample data come from a pop
> Describe what is meant by an experiment that has a completely randomized design.
> Hector obtained a random sample of twenty recent college graduates who own cars and asked each to disclose the age of their car (in months). Is it reasonable to conclude that age of car is normally distributed? The normal probability plot is shown below
> Use the results in the table to (a) draw a normal plot, (b) determine the linear correlation between the observed values and expected z-scores, (c) determine the critical value in Table VI to assess the normality of the data.
> A school psychologist wants to test the effectiveness of a new method for teaching reading. She recruits 500 first-grade students in District 203 and randomly divides them into two groups. Group 1 is taught by means of the new method, while group 2 is ta
> A casino manager wants to inspect a sample of 14 slot machines in his casino for quality-control purposes. There are 600 sequentially numbered slot machines operating in the casino. Obtain a systematic sample of 14 slot machines. Be sure to discuss how y
> According to a Gallup poll, 46% of Americans 18 years old or older stated that they had read at least six books (fiction and nonfiction) within the past year. You conduct a random sample of 250 Americans 18 years old or older and ask the individuals to d
> A farmer has a 500-acre orchard in Florida. Each acre is subdivided into blocks of 5. Altogether, there are 2500 blocks of trees on the farm. After a frost, he wants to get an idea of the extent of the damage. Obtain a sample of 10 blocks of trees using
> According to Major League Baseball rules, the ball must weigh between 5 and 5.25 ounces. A factory produces baseballs whose weights are approximately normally distributed, with mean 5.11 ounces and standard deviation 0.062 ounce. Source: www.baseball-alm
> A congresswoman wants to survey her constituency regarding public policy. She asks one of her staff members to obtain a sample of residents of the district. The frame she has available lists 9012 Democrats, 8302 Republicans, and 3012 Independents. Obtain
