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| m432 | Fairfield Homes is developing two parcels near Pigeon Fork, Tennessee. In order to test different advertising approaches, it uses different media to reach potential buyers. The mean annual family income for 15 people making inquiries at the first development is $150,000, with a standard deviation of $40,000. A corresponding sample of 25 people at the second development had a mean of $180,000, with a standard deviation of $30,000. Assume the population standard deviations are the same. At the .05 significance level, can Fairfield conclude that the population means are different? |
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| m433 | Families USA, a monthly magazine that discusses issues related to health and health costs, surveyed 20 of its subscribers. It found that the annual health insurance premiums for a family with coverage through an employer averaged $10,979. The standard deviation of the sample was $1,000.
a. Based on this sample information, develop a 90% confidence interval for the population mean yearly premium.
b. How large a sample is needed to find the population mean within $250 at 99% confidence? |
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| m434 | Far West University offers both day and evening classes in business administration. One question in a survey of students inquires how they perceive the prestige associated with eight careers. A day student was asked to rank the careers from 1 to 8, with 1 having the most prestige and 8 the least prestige. An evening student was asked to do the same. The results follow.
Find Spearman’s coefficient of rankcorrelation. |
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| m435 | Fashion Industries randomly tests its employees throughout the year. Last year in the 400 random tests conducted, 14 employees failed the test. Develop a 99% confidence interval for the proportion of applicants that fail the test. Would it be reasonable to conclude that 5% of the employees cannot pass the random drug test? Explain. |
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| m436 | Fast Service Truck Lines uses the Ford Super Duty F-750 exclusively. Management made a study of the maintenance costs and determined the number of miles traveled during the year followed the normal distribution. The mean of the distribution was 60,000 miles and the standard deviation 2,000 miles.
a. What percent of the Ford Super Duty F-750s logged 65,200 miles or more?
b. What percent of the trucks logged more than 57,060 but less than 58,280 miles?
c. What percent of the Fords traveled 62,000 miles or less during the year?
d. Is it reasonable to conclude that any of the trucks were driven more than 70,000 miles?
Explain. |
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| m437 | A fault-tolerant system that processes transactions for a financial services firm uses three separate computers. If the operating computer fails, one of the two spares can be immediately switched online. After the second computer fails, the last computer can be immediately switched online. Assume that the probability of a failure during any transaction is and that the transactions can be considered to be independent events.
(a) What is the mean number of transactions before all computers have failed?
(b) What is the variance of the number of transactions before all computers have failed? |
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| m444 | Flaws occur in the interior of plastic used for automobiles according to a Poisson distribution with a mean of 0.02 flaw per panel.
(a) If 50 panels are inspected, what is the probability that there are no flaws? (b) What is the expected number of panels that need to be inspected before a flaw is found?
(c) If 50 panels are inspected, what is the probability that the number of panels that have one or more flaws is less than or equal to 2? |
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| m445 | Following are the quantities and prices for the years 2000 and 2014 for Kinzua Valley Geriatrics. Use 2000 as the base period.
a. Determine the simple price indexes.
b. Determine the simple aggregate price index price index. for the two years.
c. Determine Laspeyres price index.
d. Determine the Paasche
e. Determine Fisher’s idealindex. |
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| m446 | For a recent year, the mean fare to fly from Charlotte, North Carolina, to Chicago, Illinois, on a discount ticket was $267. A random sample of 13 round-trip discount fares on this route last month gives: |
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| m447 | For a sample of 32 large U.S. cities, the correlation between the mean number of square feet per office worker and the mean monthly rental rate in the central business district is 2.363. At the .05 significance level, can we conclude that there is a negative association between the two variables? |
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| m448 | For each of the 32 National Football League teams, the numbers of points scored and allowed during the 2012 season are shown below.
Assuming these are sample data, answer the following questions. You may use statistical software to assist you.
a. What is the correlation coefficient between these variables? Are you surprised the association is negative? Interpret your results.
b. Find the coefficient of determination. What does it say about the relationship?
c. At the .05 significance level, can you conclude there is a negative association between “points scored” and “points allowed”?
d. At the .05 significance level, can you conclude there is a negative association between “points scored” and “points allowed” for eachconference? |
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| m449 | For each of the following, determine whether the group is a sample or a population.
a. The participants in a study of a new cholesterol drug.
b. The drivers who received a speeding ticket in Kansas City last month.
c. Those on welfare in Cook County (Chicago), Illinois.
d. The 30 stocks that make up the Dow Jones Industrial Average. |
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| m450 | For each of the following indicate whether the random variable is discrete or continuous.
a. The length of time to get a haircut.
b. The number of cars a jogger passes each morning while running.
c. The number of hits for a team in a high school girls’ softball game.
d. The number of patients treated at the South Strand Medical Center between 6 and
10 p.m. each night.
e. The distance your car traveled on the last fill-up.
f. The number of customers at the Oak Street Wendy’s who used the drive-through facility.
g. The distance between Gainesville, Florida, and all Florida cities with a population of at least 50,000. |
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| m451 | For each scenario described below, state whether or not the binomial distribution is a reasonable model for the random variable and why. State any assumptions you make.
(a) A production process produces thousands of temperature transducers. Let X denote the number of nonconforming transducers in a sample of size 30 selected at random from the process.
(b) From a batch of 50 temperature transducers, a sample of size 30 is selected without replacement. Let X denote the number of nonconforming transducers in the sample.
(c) Four identical electronic components are wired to a controller that can switch from a failed component to one of the remaining spares. Let X denote the number of components that have failed after a specified period of operation.
(d) Let X denote the number of accidents that occur along the federal highways in Arizona during a one-month period.
(e) Let X denote the number of correct answers by a student taking a multiple choice exam in which a student can eliminate some of the choices as being incorrect in some questions and all of the incorrect choices in other questions.
(f) Defects occur randomly over the surface of a semiconductor chip. However, only 80% of defects can be found by testing. A sample of 40 chips with one defect each is tested. Let X denote the number of chips in which the test finds a defect.
(g) Reconsider the situation in part (f). Now, suppose the sample of 40 chips consists of chips with 1 and with 0 defects.
(h) |
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| m452 | For many years, TV executives used the guideline that 30% of the audience were watching each of the traditional big three prime-time networks and 10% were watching cable stations on a weekday night. A random sample of 500 viewers in the Tampa–St. Petersburg, Florida, area last Monday night showed that 165 homes were tuned in to the ABC affiliate, 140 to the CBS affiliate, and 125 to the NBC affiliate, with the remainder viewing a cable station. At the .05 significance level, can we conclude that the guideline is still reasonable? |
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| m453 | For the daily lottery game in Illinois, participants select three numbers between 0 and 9. A number cannot be selected more than once, so a winning ticket could be, say, 307 but not
337. Purchasing one ticket allows you to select one set of numbers. The winning numbers are announced on TV each night.
a. How many different outcomes (three-digit numbers) are possible?
b. If you purchase a ticket for the game tonight, what is the likelihood you will win?
c. Suppose you purchase three tickets for tonight’s drawing and select a different number for each ticket. What is the probability that you will not win with any of the tickets? |
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| m454 | For the following situations, would you collect information using a sample or a population?
Why?
a. Statistics 201 is a course taught at a university. Professor Rauch has taught nearly 1,500 students in the course over the past 5 years. You would like to know the average grade for the course.
b. As part of a research project, you need to report the average profit as a percentage of revenue for the #1-ranked corporation in the Fortune 500 for each of the last 10 years.
c. You are looking forward to graduation and your first job as a salesperson for one of five large pharmaceutical corporations. Planning for your interviews, you will need to know about each company’s mission, profitability, products, and markets.
d. You are shopping for a new MP3 music player such as the Apple iPod. The manufacturers advertise the number of music tracks that can be stored in the memory. Usually, the advertisers assume relatively short, popular songs to estimate the number of tracks that can be stored. You, however, like Broadway musical tunes and they are much longer.
You would like to estimate how many Broadway tunes will fit on your MP3 player. |
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| m455 | For your e-mail, you use a filter to block spam from your inbox. The number of items blocked by day of week is recorded and Minitab is used to perform the analysis that follows. Here are the results:
Using the ANOVA results, compare the average number of items blocked for each day of theweek. |
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| m456 | Forty percent of the homes constructed in the Quail Creek area include a security system.
Three homes are selected at random:
a. What is the probability all three of the selected homes have a security system?
b. What is the probability none of the three selected homes has a security system?
c. What is the probability at least one of the selected homes has a security system?
d. Did you assume the events to be dependent or independent? |
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| m457 | Four bits are transmitted over a digital communications channel. Each bit is either distorted or received without distortion. Let Ai denote the event that the ith bit is distorted,
i = 1,.., 4.
(a) Describe the sample space for this experiment.
(b) Are the Ai’s mutually exclusive?
Describe the outcomes in each of the following events:
(c) A 1
(d) 1’
(e) A1 ∩ A2 ∩ A3 ∩ A4
(f) (A1 ∩ A2) U (A3 ∩ A4) |
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