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| m684 | Messages that arrive at a service center for an information systems manufacturer have been classified on the basis of the number of keywords (used to help route messages) and the type of message, either email or voice. Also, 70% of the messages arrive via email and the rest are voice. |
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| m685 | Messages arrive to a computer server according to a Poisson distribution with a mean rate of 10 per hour. Determine the length of an interval of time such that the probability that no messages arrive during this interval is 0.90. |
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| m686 | Midland National Bank selected a sample of 40 student checking accounts. Below are their end-of-the-month balances.
a. Tally the data into a frequency distribution using $100 as a class interval and $0 as the starting point.
b. Draw a cumulative frequency polygon.
c. The bank considers any student with an ending balance of $400 or more a “preferred customer.” Estimate the percentage of preferred customers.
d. The bank is also considering a service charge to the lowest 10% of the ending balances. What would you recommend as the cutoff point between those who have to pay a service charge and those who donot? |
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| m687 | Mike Wilde is president of the teachers’ union for Otsego School District. In preparing for upcoming negotiations, he would like to investigate the salary structure of classroom teachers in the district. He believes there are three factors that affect a teacher’s salary: years of experience, a rating of teaching effectiveness given by the principal, and whether the teacher has a master’s degree. A random sample of 20 teachers resulted in the following data.
a. Develop a correlation matrix. Which independent variable has the strongest correlation with the dependent variable? Does it appear there will be any problems with multicollinearity?
b. Determine the regression equation. What salary would you estimate for a teacher with 5 years’ experience, a rating by the principal of 60, and no master’s degree?
c. Conduct a global test of hypothesis to determine whether any of the regression coefficients differ from zero. Use the .05 significance level.
d. Conduct a test of hypothesis for the individual regression coefficients. Would you consider deleting any of the independent variables? Use the .05 significance level.
e. If your conclusion in part (d) was to delete one or more independent variables, run the analysis again without those variables.
f. Determine the residuals for the equation of part (e). Use a stem-and-leaf chart or a histogram to verify that the distribution of the residuals is approximately normal.
g. Plot the residuals computed in part (f) in a scatter d |
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| m688 | Molly’s Candle Shop has several retail stores in the coastal areas of North and South Carolina. Many of Molly’s customers ask her to ship their purchases. The following chart shows the number of packages shipped per day for the last 100 days.
a. What is this chart called?
b. What is the total number of frequencies?
c. What is the class interval?
d. What is the class frequency of the 10 up to 15 class?
e. What is the relative frequency of the 10 up to 15 class?
f. What is the midpoint of the 10 up to 15 class?
g. On how many days were there 25 or more packagesshipped? |
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| m689 | Most air travelers now use e-tickets. Electronic ticketing allows passengers to not worry about a paper ticket, and it costs the airline companies less to handle than paper ticketing. However, in recent times the airlines have received complaints from passengers regarding their e-tickets, particularly when connecting flights and a change of airlines were involved. To investigate the problem, an independent watchdog agency contacted a random sample of 20 airports and collected information on the number of complaints the airport had with e-tickets for the month of March. The information is reported below.
At the .05 significance level, can the watchdog agency conclude the mean number of complaints per airport is less than 15 per month?
a. What assumption is necessary before conducting a test of hypothesis?
b. Plot the number of complaints per airport in a frequency distribution or a dot plot. Is it reasonable to conclude that the population follows a normal distribution?
c. Conduct a test of hypothesis and interpret theresults. |
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| m690 | Most four-year automobile leases allow up to 60,000 miles. If the lessee goes beyond this amount, a penalty of 20 cents per mile is added to the lease cost. Suppose the distribution of miles driven on four-year leases follows the normal distribution. The mean is 52,000 miles and the standard deviation is 5,000 miles.
a. What percent of the leases will yield a penalty because of excess mileage?
b. If the automobile company wanted to change the terms of the lease so that 25% of the leases went over the limit, where should the new upper limit be set?
c. One definition of a low-mileage car is one that is 4 years old and has been driven less than 45,000 miles. What percent of the cars returned are considered low-mileage? |
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| m691 | Mr. James McWhinney, president of Daniel-James Financial Services, believes there is a relationship between the number of client contacts and the dollar amount of sales. To document this assertion, Mr. McWhinney gathered the following sample information. The x column indicates the number of client contacts last month and the y column shows the value of sales ($ thousands) last month for each client sampled.
a. Determine the regression equation.
b. Determine the estimated sales if 40 contacts aremade. |
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| m692 | Mr. William Profit is studying companies going public for the first time. He is particularly interested in the relationship between the size of the offering and the price per share. A sample of 15 companies that recently went public revealed the following information.
a. Determine the regression equation.
b. Conduct a test to determine whether the slope of the regression line is positive.
c. Determine the coefficient of determination. Do you think Mr. Profit should be satisfied with using the size of the offering as the independentvariable? |
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| m693 | Ms. Bergen is a loan officer at Coast Bank and Trust. From her years of experience, she estimates that the probability is .025 that an applicant will not be able to repay his or her installment loan. Last month she made 40 loans.
a. What is the probability that three loans will be defaulted?
b. What is the probability that at least three loans will be defaulted? |
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| m694 | Ms. Gene Dempsey manages the emergency care center at Bell Grove Medical Center. One of her responsibilities is to have enough nurses so that incoming patients needing service can be handled promptly. It is stressful for patients to wait a long time for emergency care even when their care needs are not life threatening. Ms. Dempsey gathered the following information regarding the number of patients over the last several weeks. The center is not open on weekends. Does it appear that there are any differences in the number of patients served by the day of the week? If there are differences, which days seem to be the busiest? Write a brief report summarizing yourfindings. |
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| m695 | Ms. Lisa Monnin is the budget director for Nexus Media Inc. She would like to compare the daily travel expenses for the sales staff and the audit staff. She collected the following sample information.
At the .10 significance level, can she conclude that the mean daily expenses are greater for the sales staff than the audit staff? What is thep-value? |
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| m696 | Ms. Maria Wilson is considering running for mayor of the town of Bear Gulch, Montana.
Before completing the petitions, she decides to conduct a survey of voters in Bear Gulch.
A sample of 400 voters reveals that 300 would support her in the November election.
a. Estimate the value of the population proportion.
b. Develop a 99% confidence interval for the population proportion.
c. Interpret your findings. |
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| m697 | A multiple choice test contains 25 questions, each with four answers. Assume a student just guesses on each question.
(a) What is the probability that the student answers more than 20 questions correctly?
(b) What is the probability the student answers less than 5 questions correctly? |
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| m698 | Near the time of an election, a cable news service performs an opinion poll of 1,000 probable voters. It shows that the Republican contender has an advantage of 52% to 48%.
a. Develop a 95% confidence interval for the proportion favoring the Republican candidate.
b. Estimate the probability that the Democratic candidate is actually leading.
c. Repeat the above analysis based on a sample of 3,000 probable voters. |
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| m699 | A new analytical method to detect pollutants in water is being tested. This new method of chemical analysis is important because, if adopted, it could be used to detect three different contaminants—organic pollutants, volatile solvents, and chlorinated compounds—instead of having to use a single test for each pollutant. The makers of the test claim that it can detect high levels of organic pollutants with 99.7% accuracy, volatile solvents with 99.95% accuracy, and chlorinated compounds with 89.7% accuracy. If a pollutant is not present, the test does not signal. Samples are prepared for the calibration of the test and 60% of them are contaminated with organic pollutants, 27% with volatile solvents, and 13% with traces of chlorinated compounds.
A test sample is selected randomly. (a) What is the probability that the test will signal?
(b) If the test signals, what is the probability that chlorinated compounds are present? |
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| m700 | New designs for a wastewater treatment tank have proposed three possible shapes, four possible sizes, three locations for input valves, and four locations for output valves. How many different product designs are possible? |
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| m701 | Nike’s annual report says that the average American buys 6.5 pairs of sports shoes per year. Suppose the population standard deviation is 2.1 and that a sample of 81 customers will be examined next year.
a. What is the standard error of the mean in this experiment?
b. What is the probability that the sample mean is between 6 and 7 pairs of sports shoes?
c. What is the probability that the difference between the sample mean and the population mean is less than 0.25 pair?
d. What is the likelihood the sample mean is greater than 7 pairs? |
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| m702 | Nine observations were randomly selected from population A and eight observations were randomly selected from population B. The populations are not necessarily normally distributed. Use the .05 significance level, a two-tailed test, and the Wilcoxon rank-sum test to determine whether there is a difference between the two populations.
Population A ....... 12, 14, 15, 19, 23, 29, 33, 40, 51
Population B ...... 13, 16, 19, 21, 22, 33, 35, 43 |
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| m703 | On page 641 at the beginning of this chapter, we presented a graph showing the price per gallon of gasoline from 1990 until 2012. The actual data for each year are given below.
Determine the trend line using both linear and nonlinear equations. Which would you suggest? Why? Based on your recommendation as the better equation, what cost per gallon would you estimate for 2013 and2014? |
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