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mathematics
statistics

Introductory Statistics 8th Edition Prem S. Mann - Solutions

According to a report in the Wall Street Journal (online.wsj.com/mdc/public/page/2_3022 auto sales. html), the distribution of all auto sales by segment (type of vehicle) in the United States during November 2011 was as follows:A recent survey of 730 new auto sales had the following
One of the products produced by Branco Food Company is Total-Bran Cereal, which competes with three other brands of similar total-bran cereals. The company’s research office wants to investigate if the percentage of people who consume total-bran cereal is the same for each of these four brands.
The percentage distribution of birth weights for all children in cases of multiple births (twins, triplets, etc.) in North Carolina during 2009 was as given in the following table:The frequency distribution of birth weights of a sample of 587 children who shared multiple births and were born in
A 2010 poll by Marist University asked people to choose their favorite classic Christmas movie from a list of five choices. The following table shows the frequencies for the various movies:Test at a 1% significance level whether these five movies are equally preferred.
During a bear market, 140 investors were asked how they were adjusting their portfolios to protect themselves. Some of these investors were keeping most of their money in stocks, whereas others were shifting large amounts of money to bonds, real estate, or cash (such as money market accounts). The
A randomly selected sample of 100 persons who suffer from allergies were asked during what season they suffer the most. The results of the survey are recorded in the following table.Using a 1% significance level, test the null hypothesis that the proportions of all allergic persons are equally
All shoplifting cases in the town of Seven Falls are randomly assigned to either Judge Stark or Judge Rivera. A citizens group wants to know whether either of the two judges is more likely to sentence the offenders to jail time. A sample of 180 recent shoplifting cases produced the following
A November 2011 Kaiser Family Foundation study asked a random sample of Americans what they would like to see done with the American Healthcare Act. The following table lists the frequencies of the results that are comparable to those found in the study:Test at a 5% significance level whether
In the National Survey on Drug Use and Health, one of the questions asked is about illicit drug use by Americans age 18 to 25 years (www.samhsa.gov/data/NSDUH/2k10NSDUH/2k10Results.htm#Fig2-7). On the assumption that the data were based on random samples of 3600 people in each of the years 2008 to
Recent recession and bad economic conditions forced many people to hold more than one job to make ends meet. A sample of 500 persons who held more than one job produced the followingTest at a 1% significance level whether gender and marital status are related for all people who hold more than one
Find the value of x2 for 4 degrees of freedom and a. .005 area in the right tail of the chi-square distribution curve b. .05 area in the left tail of the chi-square distribution curve
ATVs (all-terrain vehicles) have become a source of controversy. Some people feel that their use should be tightly regulated, while others prefer fewer restrictions. Suppose a survey consisting of a random sample of 200 people aged 18 to 27 and another survey of a random sample of 210 people aged
A random sample of 100 persons was selected from each of four regions in the United States. These people were asked whether or not they support a certain farm subsidy program. The results of the survey are summarized in the following table.Using a 1% significance level, test the null hypothesis
Construct the 98% confidence intervals for the population variance and standard deviation for the following data, assuming that the respective populations are (approximately) normally distributed. a. n = 21, s2 = 9.2 b. n = 17, s2 = 1.7
Construct the 95% confidence intervals for the population variance and standard deviation for the following data, assuming that the respective populations are (approximately) normally distributed. a. n = 10, s2 = 7.2 b. n = 18, s2 = 14.8
Refer to Exercise 11.62a. Test at a 5% significance level if the population variance is different from 6.5. n = 21, s2 = 9.2
Refer to Exercise 11.62b. Test at a 2.5% significance level if the population variance is greater than 1.1. n = 17, s2 = 1.7
Refer to Exercise 11.63a. Test at a 1% significance level if the population variance is greater than 4.2. n = 10, s2 = 7.2
Refer to Exercise 11.63b. Test at a 5% significance level if the population variance is different from 10.4. n = 18, s2 = 14.8
Usually people do not like waiting in line for a long time for service. A bank manager does not want the variance of the waiting times for her customers to be greater than 4.0 square minutes. A random sample of 25 customers taken from this bank gave the variance of the waiting times equal to 8.3
The variance of the SAT scores for all students who took that test this year is 5000. The variance of the SAT scores for a random sample of 20 students from one school is equal to 3175. a. Test at a 2.5% significance level whether the variance of the SAT scores for students from this school is
Determine the value of x2 for 13 degrees of freedom and a. .025 area in the left tail of the chi-square distribution curve b. .995 area in the right tail of the chi-square distribution curve
A company manufactures ball bearings that are supplied to other companies. The machine that is used to manufacture these ball bearings produces them with a variance of diameters of .025 square millimeter or less. The quality control officer takes a sample of such ball bearings quite often and
A random sample of 25 students taken from a university gave the variance of their GPAs equal to .19. a. Construct the 99% confidence intervals for the population variance and standard deviation. Assume that the GPAs of all students at this university are (approximately) normally distributed. b. The
A sample of seven passengers boarding a domestic flight produced the following data on weights (in pounds) of their carry-on bags.a. Using the formula from Chapter 3, find the sample variance, s2, for these data. b. Make the 98% confidence intervals for the population variance and standard
The following are the prices (in dollars) of the same brand of camcorder found at eight stores inLos Angeles.a. Using the formula from Chapter 3, find the sample variance, s2, for these data. b. Make the 95% confidence intervals for the population variance and standard deviation. Assume that the
A 2009 survey reported in USA TODAY asked U.S. households who cooks in their homes on Mother€™s Day. The results from the survey are reported in the following table. Assume that these results are true for the population of all U.S. households in 2009.Suppose that recently a random sample
A chemical manufacturing company wants to locate a hazardous waste disposal site near a city of 50,000 residents and has offered substantial financial inducements to the city. Two hundred adults (110 women and 90 men) who are residents of this city are chosen at random. Sixty percent of these
A student who needs to pass an elementary statistics course wonders whether it will make a difference if she takes the course with instructor A rather than instructor B. Observing the final grades given by each instructor in a recent elementary statistics course, she finds that Instructor A gave 48
Each of five boxes contains a large (but unknown) number of red and green marbles. You have been asked to find if the proportions of red and green marbles are the same for each of the five boxes. You sample 50 times, with replacement, from each of the five boxes and observe 20, 14, 23, 30, and 18
Suppose that you have a two-way table with the following row and column totals.The observed values in the cells must be counts, which are nonnegative integers. Calculate the expected counts for the cells under the assumption that the two variables are independent. Based on your calculations,
You have collected data on a variable, and you want to determine if a normal distribution is a reasonable model for these data. The following table shows how many of the values fall within certain ranges of z values for these data.Perform a hypothesis test to determine if a normal distribution is
Describe the four characteristics of a multinomial experiment.
Refer to Problem 11.61. Explain why the hypothesis test in that problem is a test of homogeneity as opposed to a test of independence. What feature of the data would change if you were to collect data in order to test for independence?
You are performing a goodness-of-fit test with four categories, all of which are supposed to be equally likely. You have a total of 100 observations. The observed frequencies are 21, 26, 31, and 22, respectively, for the four categories. a. Show that you would fail to reject the null hypothesis for
Multiple choice questions: 1. The random variable x2 assumes only a. Positive b. Nonnegative c. Non-positive values 2. The parameter(s) of the chi-square distribution is (are) a. Degrees of freedom b. df and n c. x2 3. Which of the following is not a characteristic of a multinomial experiment? a.
According to the Henry J. Kaiser Family Foundation (www.statehealthfacts.org), the percentage distribution of the source of health insurance in the United States in 2010 was as listed in the following table.Recently 15,000 randomly selected Americans were asked about the source of their health
The following table gives the two-way classification of 1000 persons who have been married at least once. They are classified by educational level and marital status.Test at a 1% significance level whether educational level and ever being divorced are dependent.
A researcher wanted to investigate if people who belong to different income groups are homogeneous with regard to playing lotteries. She took a sample of 600 people from the low-income group, another sample of 500 people from the middle-income group and a third sample of 400 people from the high
The owner of an ice cream parlor is concerned about consistency in the amount of ice cream his servers put in each cone. He would like the variance of all such cones to be no more than .25 square ounces. He decides to weigh each double-dip cone just before it is given to the customer. For a sample
Surfer Dude swimsuit company plans to produce a new line of quick-dry swimsuits. Three textile companies are competing for the company€™s quick-dry fabric contract. To check the fabrics of the three companies, Surfer Dude selected 10 random swatches of fabric from each company, soaked
A university employment office wants to compare the time taken by graduates with three different majors to find their first full-time job after graduation. The following table lists the time (in days) taken to find their first full-time job after graduation for a random sample of eight business
A consumer agency wanted to find out if the mean time taken by each of three brands of medicines to provide relief from a headache is the same. The first drug was administered to six randomly selected patients, the second to four randomly selected patients, and the third to five randomly selected
A large company buys thousands of light bulbs every year. The company is currently considering four brands of light bulbs to choose from. Before the company decides which light bulbs to buy, it wants to investigate if the mean lifetimes of the four types of light bulbs are the same. The
The following table lists the numbers of violent crimes reported to police on randomly selected days for this year. The data are taken from three large cities of about the same size.Using a 5% significance level, test the null hypothesis that the mean number of violent crimes reported per day is
A music company collects data from customers who purchase CDs and MP3 downloads from them. Each person is asked to state his or her favorite musical genre from the following list: Classic Rock, Country, Hip-Hop/Rap, Jazz, Pop, and R&B. Random samples of customers were selected from each genre. Each
A local car dealership is interested in determining how successful their salespeople are in turning a profit when selling a car. Specifically, they are interested in the average percentage of price markups earned on various car sales. The following table lists the percentages of price markups for a
A farmer wants to test three brands of weight-gain diets for chickens to determine if the mean weight gain for each of these brands is the same. He selected 15 chickens and randomly put each of them on one of these three brands of diet. The following table lists the weights (in pounds) gained by
An ophthalmologist is interested in determining whether a golfer€™s type of vision (far-sightedness, near-sightedness, no prescription) impacts how well he or she can judge distance. Random samples of golfers from these three groups (far-sightedness, near-sightedness, no prescription)
A resort area has three seafood restaurants, which employ students during the summer season. The local chamber of commerce took a random sample of five servers from each restaurant and recorded the tips they received on a recent Friday night. The results (in dollars) of the survey are shown in the
A student who has a 9 A.M. class on Monday, Wednesday, and Friday mornings wants to know if the mean time taken by students to find parking spaces just before 9 A.M. is the same for each of these three days of the week. He randomly selects five weeks and records the time taken to find a parking
A billiards parlor in a small town is open just 4 days per week€”Thursday through Sunday. Revenues vary considerably from day to day and week to week, so the owner is not sure whether some days of the week are more profitable than others. He takes random samples of 5 Thursdays, 5 Fridays,
Suppose that you are a reporter for a newspaper whose editor has asked you to compare the hourly wages of carpenters, plumbers, electricians, and masons in your city. Since many of these workers are not union members, the wages vary considerably among individuals in the same trade. a. What data
The editor of an automotive magazine has asked you to compare the mean gas mileages of city driving for three makes of compact cars. The editor has made available to you one car of each of the three makes, three drivers, and a budget sufficient to buy gas and pay the drivers for approximately 500
Do rock music CDs and country music CDs give the consumers the same amount of music listening time? A sample of 12 randomly selected single rock music CDs and a sample of 14 randomly selected single country music CDs have the following total lengths (in minutes).Assume that the two populations are
Suppose you are performing a one-way ANOVA test with only the information given in the following table.a. Suppose the sample sizes for all groups are equal. How many groups are there? What are the group sample sizes? b. The p-value for the test of the equality of the means of all populations is
Multiple choice questions: 1. The F distribution is a. Continuous b. Discrete c. Neither 2. The F distribution is always a. Symmetric b. Skewed to the right c. Skewed to the left 3. The units of the F distribution, denoted by F, are always a. Non-positive b. Positive c. Nonnegative 4. The one-way
A small college town has four pizza parlors that make deliveries. A student doing a research paper for her business management class decides to compare how promptly the four parlors deliver. On six randomly chosen nights, she orders a large pepperoni pizza from each establishment, then records the
Briefly describe the assumptions that must hold true to apply the one-way ANOVA procedure as mentioned in this chapter.
Describe the main characteristics of an F distribution.
Briefly explain when a one-way ANOVA procedure is used to make a test of hypothesis.
Describe the assumptions that must hold true to apply the one-way analysis of variance procedure to test hypotheses.
Consider the following data obtained for two samples selected at random from two populations that are independent and normally distributed with equal variances.a. Calculate the means and standard deviations for these samples using the formulas from Chapter 3. b. Using the procedure learned in
Consider the following data obtained for two samples selected at random from two populations that are independent and normally distributed with equal variances.a. Calculate the means and standard deviations for these samples using the formulas from Chapter 3. b. Using the procedure learned in
The following ANOVA table, based on information obtained for three samples selected from three independent populations that are normally distributed with equal variances, has a few missing values.a. Find the missing values and complete the ANOVA table. b. Using Î± = .01, what is your
The following ANOVA table, based on information obtained for four samples selected from four independent populations that are normally distributed with equal variances, has a few missing values.a. Find the missing values and complete the ANOVA table. b. Using Î± = .05, what is your
A clothing store chain is having a sale based on the use of a coupon. The company is interested in knowing whether the wording of the coupon affects the number of units of the product purchased by customers. The company created four coupons for the same product, each with different wording. Four
People who have home gaming systems, such as Wii„¢, Play station„¢, and Xbox„¢, are well aware of how quickly they need to replace the batteries in the remote controls. A consumer agency decided to test three major brands of alkaline batteries to determine whether they
The recommended acidity levels for sweet white wines (e.g., certain Rieslings, Port, Eiswein,Muscat) is .70% to .85% (www.grapestompers.com/articles/measure_acidity.htm). A vintner (winemaker) takes three random samples of Riesling from casks that are 15, 20, and 25 years old, respectively, and
A local €œpick-your-own€ farmer decided to grow blueberries. The farmer purchased and planted eight plants of each of the four different varieties of high bush blueberries. The yield (in pounds) of each plant was measured in the upcoming year to determine whether the average
Explain the meaning of the words simple and linear as used in simple linear regression.
The following table gives the average weekly retail price of a gallon of regular gasoline in the eastern United States over a 9-week period from December 19, 2011, through February 13, 2012. Consider these 9 weeks as a random sample.a. Assign a value of 0 to 12/19/11, of 1 to 12/16/11, of 2 to
The following table gives the completion times for the winners in the women’s 200-meter dash finals in the Summer Olympic Games from 1972 to 2008. The times are in seconds rounded to the nearest 1/100 second. Olympic Year Time (seconds) 1972.............. 22.40 1976..............
Refer to the data on ages and numbers of breakdowns for seven machines given in Exercise 13.95. Construct a 99% confidence interval for the mean number of breakdowns per month for all machines with an age of 8 years. Find a 99% prediction interval for the number of breakdowns per month for a
Refer to the data on the air pollution index and the number of emergency hospital admissions for acute respiratory problems given in Exercise 13.96. Determine a 95% confidence interval for the mean number of such emergency admissions on all days with an air pollution index of 7.0. Make a 95%
Refer to the data given in Exercise 13.97 on the number of times a specific product is promoted on the intercom system in a supermarket and the number of units of that product sold. Make a 90% confidence interval for the mean number of units of that product sold on days with 35 promotions.
Refer to the data given in Exercise 13.98 on the living area (in square feet) and price (in thousands of dollars) of 10 randomly selected houses listed for sale in a city. Construct a 98% confidence interval for the mean price of all houses with living areas of 2400 square feet. Construct a 98%
Consider the data given in the following table.a. Find the least squares regression line and the linear correlation coefficient r. b. Suppose that each value of y given in the table is increased by 5 and the x values remain unchanged. Would you expect r to increase, decrease, or remain the same?
Suppose that you work part-time at a bowling alley that is open daily from noon to midnight. Although business is usually slow from noon to 6 PM, the owner has noticed that it is better on hotter days during the summer, perhaps because the premises are comfortably air-conditioned. The owner shows
An economist is studying the relationship between the incomes of fathers and their sons or daughters. Let x be the annual income of a 30-year-old person and let y be the annual income of that person’s father at age 30 years, adjusted for inflation. A random sample of 300 thirty-year-olds and
For the past 25 years Burton Hodge has been keeping track of how many times he mows his lawn and the average size of the ears of corn in his garden. Hearing about the Pearson correlation coefficient from a statistician buddy of his, Burton decides to substantiate his suspicion that the more often
It seems reasonable that the more hours per week a full-time college student works at a job, the less time he or she will have to study and, consequently, the lower his or her GPA would be.a. Assuming a linear relationship, suggest specifically what the equation relating x and y would be, where x
Consider the formulas for calculating a prediction interval for a new (specific) value of y. For each of the changes mentioned in parts a through c below, state the effect on the width of the confidence interval (increase, decrease, or no change) and why it happens. Note that besides the change
For each of the regression lines in Exercises 13.53 through 13.56, interpret the slope in terms of the application of that exercise. In addition, state whether the value of the intercept is logical, and why it is or is not logical. If it is logical, state what the value of the intercept represents
Consider the following dataa. Calculate the correlation between x and y, and perform a hypothesis test to determine if the correlation is significantly greater than zero. Use a significance level of 5%. b. Are you willing to conclude that there is a strong linear association between the two
Explain the following. a. Population regression line b. Sample regression line c. True values of A and B d. Estimated values of A and B that are denoted by a and b, respectively
Briefly explain the assumptions of the population regression model.
Plot the following straight lines. Give the values of the y-intercept and slope for each of these lines and interpret them. Indicate whether each of the lines gives a positive or a negative relationship between x and y. a. y = 100 + 5x b. y = 400 – 4x
Plot the following straight lines. Give the values of the y-intercept and slope for each of these lines and interpret them. Indicate whether each of the lines gives a positive or a negative relationship between x and y. a. y = –60 + 8x b. y = 300 – 6x
A population data set produced the following information. N = 250, ∑x = 9880, ∑y = 1456, ∑xy = 85,080, ∑x2 = 485,870 Find the population regression line.
A population data set produced the following information. N = 460, ∑x = 3920, ∑y = 2650, ∑xy = 26,570, ∑x2 = 48,530 Find the population regression line.
The following information is obtained from a sample data set. n = 10, ∑x = 100, ∑y = 220, ∑xy = 3680, ∑x2 = 1140 Find the estimated regression line.
The following information is obtained from a sample data set. n = 12, ∑x = 66, ∑y = 588, ∑xy = 2244, ∑x2 = 396 Find the estimated regression line.
A car rental company charges $50 a day and 20 cents per mile for renting a car. Let y be the total rental charges (in dollars) for a car for one day and x be the miles driven. The equation for the relationship between x and y is y = 50 + .20x a. How much will a person pay who rents a car for one
Bob’s Pest Removal Service specializes in removing wild creatures (skunks, bats, reptiles, etc.) from private homes. He charges $70 to go to a house plus $20 per hour for his services. Let y be the total amount (in dollars) paid by a household using Bob’s services and x the number of hours Bob
A researcher took a sample of 25 electronics companies and found the following relationship between x and y, where x is the amount of money (in millions of dollars) spent on advertising by a company in 2011 and y represents the total gross sales (in millions of dollars) of that company for 2011. ŷ
A researcher took a sample of 10 years and found the following relationship between x and y, where x is the number of major natural calamities (such as tornadoes, hurricanes, earthquakes, floods, etc.) that occurred during a year and y represents the average annual total profits (in millions of
An auto manufacturing company wanted to investigate how the price of one of its car models depreciates with age. The research department at the company took a sample of eight cars of this model and collected the following information on the ages (in years) and prices (in hundreds of dollars) of
The following table gives information on the amount of sugar (in grams) and the calorie count in one serving of a sample of 13 varieties of Kellogg€™s cereal.a. Construct a scatter diagram for these data. Does the scatter diagram exhibit a linear relationship between the amount of sugar
The following table contains information on the amount of time that each of 12 students spends each day (on average) on social networks (Facebook, Twitter, etc.) and the Internet for social or entertainment purposes and his or her grade point average (GPA).a. Construct a scatter diagram for these

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