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theory of statistics

Questions and Answers of Theory of Statistics

The same study of church contributions in Scandia revealed that 15 of the 40 families sampled attend church regularly. Construct the 95 percent confidence interval for the proportion of families
Thirty-six items are randomly selected from a population of 300 items. The sample mean is 35 and the sample standard deviation 5.Develop a 95 percent confidence interval for the population mea
There are 250 families in Scandia, Pennsylvania. A random sample of 40 of these families revealed the mean annual church contribution was $450 and the standard deviation of this was $75.Could the
The Fox TV network is considering replacing one of its prime-time crime investigation shows with a new family-oriented comedy show.Before a final decision is made, network executives commission a
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
The owner of the West End Kwick Fill Gas Station wishes to determine the proportion of customers who use a credit card or debit card to pay at the pump. He surveys 100 customers and finds that 80
A market survey was conducted to estimate the proportion of homemakers who would recognize the brand name of a cleanser based on the shape and the color of the container. Of the 1,400 homemakers
The union representing the Bottle Blowers of America (BBA)is considering a proposal to merge with the Teamsters Union.According to BBA union bylaws, at least three-fourths of the union membership
The Greater Pittsburgh Area Chamber of Commerce wants to estimate the mean time workers who are employed in the downtown area spend getting to work. A sample of 15 workers reveals the following
Merrill Lynch Securities and Health Care Retirement, Inc., are two large employers in down-town Toledo, Ohio. They are considering jointly offering child care for their employees. As a part of the
Use Appendix B.2 to locate the value of t under the following conditions.a. The sample size is 15 and the level of confidence is 95 percent.b. The sample size is 24 and the level of confidence is 98
Use Appendix B.2 to locate the value of t under the following conditions.a. The sample size is 12 and the level of confidence is 95 percent.b. The sample size is 20 and the level of confidence is 90
The manager of the Inlet Square Mall, near Ft. Myers, Florida, wants to estimate the mean amount spent per shopping visit by customers. A sample of 20 customers reveals the following amounts
A tire manufacturer wishes to investigate the tread life of its tires. A sample of 10 tires driven 50,000 miles revealed a sample mean of 0.32 inch of tread remaining with a standard deviation of
Dottie Kleman is the “Cookie Lady.” She bakes and sells cookies at 50 different locations in the Philadelphia area. Ms. Kleman is concerned about absenteeism among her workers. The information
Dr. Patton is a professor of English. Recently she counted the number of misspelled words in a group of student essays. She noted the distribution of misspelled words per essay followed the normal
Bob Nale is the owner of Nale’s Texaco GasTown. Bob would like to estimate the mean number of gallons of gasoline sold to his customers. Assume the number of gallons sold follows the normal
Refer to the previous exercise. Suppose that 64 smokers (instead of 49) were sampled. Assume the sample mean remained the same.a. What is the 95 percent confidence interval estimate of μ?b. Explain
A research firm conducted a survey to determine the mean amount steady smokers spend on cigarettes during a week. They found the distribution of amounts spent per week followed the normal
Suppose you want an 85 percent confidence level. What value would you use to multiply the standard error of the mean by?
A sample of 81 observations is taken from a normal population with a standard deviation of 5. The sample mean is 40. Determine the 95 percent confidence interval for the population mean
A sample of 49 observations is taken from a normal population with a standard deviation of 10. The sample mean is 55. Determine the 99 percent confidence interval for the population mean.
The Bun-and-Run is a franchise fast-food restaurant located in the Northeast specializing in half-pound hamburgers, fish sandwiches, and chicken sandwiches. Soft drinks and french fries are also
From many years in the automobile leasing business, Town Bank knows the mean distance driven on a four-year lease is 50,000 miles and the standard deviation is 5,000. Suppose, using the MINITAB
The American Management Association wishes to have information on the mean income of middle managers in the retail industry. A random sample of 256 managers reveals a sample mean of$45,420. The
Define level of confidence.
Define a point estimate.
Refer to the CIA data, which report demographic and economic information on 46 countries. Select a random sample of 10 countries.For this sample calculate the mean GDP/capita. Repeat this sampling
Refer to the Real Estate data, which report information on the homes sold in the Denver, Colorado, area last year.a. Compute the mean and the standard deviation of the distribution of the selling
There are several websites that will report the 30 stocks that make up the Dow Jones Industrial Average (DJIA). One site is http://www.bloomberg.com/markets/stocks/movers_index_dow.ht.Compute the
You need to find the “typical” or mean annual dividend per share for large banks. You decide to sample six banks listed on the New York Stock Exchange. These banks and their trading symbols
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
The Oil Price Information Center reports the mean price per gallon of regular gasoline is $3.26 with a population standard deviation of$0.18. Assume a random sample of 40 gasoline stations is
Over the past decade the mean number of members of the Information Systems Security Association who have experienced a denial-of-service attack each year is 510 with a standard deviation of 14.28
Human Resource Consulting (HRC) is surveying a sample of 60 firms in order to study health care costs for a client. One of the items being tracked is the annual deductible that employees must pay.
The following table lists the per capita personal income for each of the 50 states in 2005.a. You wish to select a sample of eight from this list. The selected random numbers are 45, 15, 81, 09, 39,
Suppose we roll a fair die two times.a. How many different samples are there?b. List each of the possible samples and compute the mean.c. On a chart similar to Chart 8–1, compare the distribution
The mean SAT score for Division I student-athletes is 947 with a standard deviation of 205. If you select a random sample of 60 of these students, what is the probability the mean is below 900?
Crossett Trucking Company claims that the mean weight of its delivery trucks when they are fully loaded is 6,000 pounds and the standard deviation is 150 pounds. Assume that the population follows
A recent study by the Greater Los Angeles Taxi Drivers Association showed that the mean fare charged for service from Hermosa Beach to Los Angeles International Airport is $18.00 and the standard
The mean age at which men in the United States marry for the first time follows the normal distribution with a mean of 24.8 years. The standard deviation of the distribution is 2.5 years. For a
Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is$110,000. This distribution follows the normal distribution with
Recent studies indicate that the typical 50-year-old woman spends$350 per year for personal-care products. The distribution of the amounts spent follows a normal distribution with a standard
CRA CDs, Inc., wants the mean lengths of the “cuts” on a CD to be 135 seconds (2 minutes and 15 seconds). This will allow the disk jockeys to have plenty of time for commercials within each
Mattel Corporation produces a remote-controlled car that requires three AA batteries. The mean life of these batteries in this product is 35.0 hours. The distribution of the battery lives closely
The Appliance Center has six sales representatives at its North Jacksonville outlet. Listed below is the number of refrigerators sold by each last month.a. How many samples of size two are
The Quality Control Department employs five technicians during the day shift. Listed below is the number of times each technician instructed the production foreman to shut down the manufacturing
At the downtown office of First National Bank there are five tellers.Last week the tellers made the following number of errors each: 2, 3, 5, 3, and 5.a. How many different samples of 2 tellers are
Suppose your statistics instructor gave six examinations during the semester. You received the following grades (percent correct): 79, 64, 84, 82, 92, and 77. Instead of averaging the six scores, the
As a part of their customer-service program, United Airlines randomly selected 10 passengers from today’s 9 a.m. Chicago–Tampa flight. Each sampled passenger is to be interviewed in depth
There are 25 motels in Goshen, Indiana. The number of rooms in each motel follows:a. Using a table of random numbers (Appendix B.6), select a random sample of five motels from this population.b.
Answer the following questions in one or two well-constructed sentences.a. What happens to the standard error of the mean if the sample size is increased?b. What happens to the distribution of the
The manufacturer of eMachines, an economy-priced computer, recently completed the design for a new laptop model. eMachine’s top management would like some assistance in pricing the new laptop. Two
List the reasons for sampling. Give an example of each reason for sampling.
What is sampling error? Could the value of the sampling error be zero? If it were zero, what would this mean?
Medical Mutual Insurance is investigating the cost of a routine office visit to family- practice physicians in the Rochester, New York, area. The following is a list of family-practice physicians in
The retail stores located in the North Towne Square Mall are:a. If the following random numbers are selected, which retail stores should be contacted for a survey? 11, 65, 86, 62, 06, 10, 12, 77, and
According to an IRS study, it takes a mean of 330 minutes for taxpayers to prepare, copy, and electronically file a 1040 tax form.This distribution of times follows the normal distribution and the
The rent for a one-bedroom apartment in Southern California follows the normal distribution with a mean of $2,200 per month and a standard deviation of $250 per month. The distribution of the monthly
A normal population has a mean of 75 and a standard deviation of 5.You select a sample of 40. Compute the probability the sample mean is:a. Less than 74.b. Between 74 and 76.c. Between 76 and 77.d.
A normal population has a mean of 60 and a standard deviation of 12. You select a random sample of 9. Compute the probability the sample mean is:a. Greater than 63.b. Less than 56.c. Between 56 and
Refer to the Cola, Inc., information. Suppose the quality technician selected a sample of 16 Jumbo bottles that averaged 31.08 ounces.What can you conclude about the filling process?
The Quality Assurance Department for Cola, Inc., maintains records regarding the amount of cola in its Jumbo bottle. The actual amount of cola in each bottle is critical, but varies a small amount
Haughton Elevator Company wishes to develop specifications for the number of people who can ride in a new oversized elevator. Suppose the mean weight for an adult is 160 pounds and the standard
A. C. Nielsen Company provides information to companies advertising on television. Prior research indicates that adult Americans watch an average of 6.0 hours per day of television. The standard
Arm and Hammer Company wants to ensure that its laundry detergent actually contains 100 fluid ounces, as indicated on the label. Historical summaries from the filling process indicate the mean amount
Consider the digits in the phone numbers on a randomly selected page of your local phone book a population. Make a frequency table of the final digit of 30 randomly selected phone numbers. For
Consider all of the coins (pennies, nickels, quarters, etc.) in your pocket or purse as a population. Make a frequency table beginning with the current year and counting backward to record the ages
Scrapper Elevator Company has 20 sales representatives who sell its product throughout the United States and Canada. The number of units sold last month by each representative is listed below. Assume
Appendix B.6 is a table of random numbers. Hence, each digit from 0 to 9 has the same likelihood of occurrence.a. Draw a graph showing the population distribution. What is the population mean?b.
Refer to the Spence Sprockets, Inc., data here. Select 10 random samples of 5 employees each. Use the methods described earlier in the chapter and the Table of Random Numbers (Appendix B.6) to find
Ed Spence began his sprocket business 20 years ago. The business has grown over the years and now employs 40 people. Spence Sprockets, Inc., faces some major decisions regarding health care for these
There are five sales associates at Mid-Motors Ford. The five representatives and the number of cars they sold last week are:a. How many different samples of size 2 are possible?b. List all possible
In the law firm Tybo and Associates, there are six partners. Listed below is the number of cases each associate actually tried in court last month.a. How many different samples of 3 are possible?b.
A population consists of the following five values: 0, 0, 1, 3, 6.a. List all samples of size 3, and compute the mean of each sample.b. Compute the mean of the distribution of sample means and the
A population consists of the following five values: 12, 12, 14, 15, and 20.a. List all samples of size 3, and compute the mean of each sample.b. Compute the mean of the distribution of sample means
A population consists of the following five values: 2, 2, 4, 4, and 8.a. List all samples of size 2, and compute the mean of each sample.b. Compute the mean of the distribution of sample means and
A population consists of the following four values: 12, 12, 14, and 16.a. List all samples of size 2, and compute the mean of each sample.b. Compute the mean of the distribution of the sample mean
The lengths of service of all the executives employed by Standard Chemicals are:(a) Using the combination formula, how many samples of size 2 are possible?(b) List all possible samples of 2
Tartus Industries has seven production employees (considered the population). The hourly earnings of each employee are given in Table 8–2.1. What is the population mean?2. What is the sampling
Listed below are the 27 Nationwide Insurance agents in the Toledo, Ohio, metropolitan area. We would like to estimate the mean number of years employed with Nationwide.a. We want to select a random
Listed below are the 35 members of the Metro Toledo Automobile Dealers Association. We would like to estimate the mean revenue from dealer service departments.a. We want to select a random sample of
The following is a list of hospitals in the Cincinnati (Ohio) and Northern Kentucky Region. Also included is whether the hospital is a general medical/surgical hospital (M/S) or a specialty hospital
The following is a list of Marco’s Pizza stores in Lucas County. Also noted is whether the store is corporate-owned (C) or manager-owned(M). A sample of four locations is to be selected and
Refer to Self-Review 8–1 and the class roster here. Suppose a systematic random sample will select every ninth student enrolled in the class. Initially, the fourth student on the list was selected
The following class roster lists the students enrolling in an introductory course in business statistics. Three students are to be randomly selected and asked various questions regarding course
Jane and Joe Miley operate the Foxtrot Inn, a bed and breakfast in Tryon, North Carolina. There are eight rooms available for rent at this B&B. Listed below is the number of these eight rooms
Define and construct a sampling distribution of the sample mean
Describe methods to select a sample.
Explain why a sample is often the only feasible way to learn something about a population.
Refer to the CIA data, which report demographic and economic information on 46 countries.a. The mean of the GDP/capita variable is 16.58 with a standard deviation of 9.27. Use the normal distribution
Refer to the Baseball 2006 data, which report information on the 30 Major League Baseball teams for the 2006 season.a. The mean attendance per team for the season was 2,533,254 with a standard
Refer to the Real Estate data, which report information on homes sold in the Denver, Colorado, area during the last year.a. The mean selling price (in $ thousands) of the homes was computed earlier
The annual sales of romance novels follow the normal distribution.However, the mean and the standard deviation are unknown. Forty percent of the time sales are more than 470,000, and 10 percent of
The price of shares of Bank of Florida at the end of trading each day for the last year followed the normal distribution. Assume there were 240 trading days in the year. The mean price was $42.00 per
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
The Cincinnati Enquirer, in its Sunday business supplement, reported that the mean number of hours worked per week by those employed full time is 43.9. The article further indicated that about
The weights of canned hams processed at Henline Ham Company follow the normal distribution, with a mean of 9.20 pounds and a standard deviation of 0.25 pounds. The label weight is given as 9.00
The funds dispensed at the ATM machine located near the checkout line at the Kroger’s in Union, Kentucky, follows a normal probability distribution with a mean of $4,200 per day and a standard
The goal at U.S. airports handling international flights is to clear these flights within 45 minutes. Let’s interpret this to mean that 95 percent of the flights are cleared in 45 minutes, so 5

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