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mathematics
statistics

Questions and Answers of Statistics

In a random sample of 400 measurements, 227 of the measurements possess the characteristic of interest, A.a. Use a 95% confidence interval to estimate the true proportion p of measurements in the
Find x2α/2 and x2(1-a/2) from Table IV, Appendix D, for each of the following: a. n = 10, α = .05 b. n = 20, α = .05 c. n = 50, α = .01
Calculate the finite population correction factor for each of the following situations: a. n = 50, N = 2,000 b. n = 20, TV = 100 c. n = 300, TV = 1,500
The Centers for Disease Control and Prevention in Atlanta, Georgia, conducts an annual survey of the general health of the U.S. population as part of its Behavioral Risk Factor Surveillance System.
Health care workers who use latex gloves with glove powder on a daily basis are particularly susceptible to developing a latex allergy. Symptoms of a latex allergy include conjunctivitis, hand
For more than 20 years, the Occupational Safety & Health Administration has required companies that handle hazardous chemicals to complete material safety data sheets (MSDSs). These MSDSs have been
Recall that 106 shoppers at a shopping mall in Muncie, Indiana, responded to the question, '"Made in the USA' means what percentage of U.S. labor and materials?" Sixty-four shoppers answered,
The EPA wants to test a randomly selected sample of n water specimens and estimate the mean daily rate of pollution produced by a mining operation. If the EPA wants a 95% confidence interval estimate
Periodically, the Hillsborough County (Florida) Water Department tests the drinking water of homeowners for contaminants such as lead and copper. The lead and copper levels in water specimens
According to the New Jersey Governor's Council for a Drug-Free Workplace Report, 50 of the 72 sampled businesses that are members of the council admitted that they had employees with substance abuse
A company is interested in estimating p, the mean number of days of sick leave taken by all its employees. The firm's statistician selects at random 100 personnel files and notes the number of sick
Refer to the Journal of Relationship Marketing (Vol. 7, 2008) study of the prevalence of blogs and forums at Fortune 500 firms with both English and Chinese Web sites. In a sample of 56 firms that
Consider the quantitative variable, number of carats, recorded for each of the 308 diamonds for sale on the open market.a. Select a random sample of 30 diamonds from the 308 diamonds.b. Find the mean
The U.S. Army Corps of Engineers data on a sample of 144 contaminated fish collected from the river adjacent to a chemical plant. Estimate the proportion of contaminated fish that are of the channel
Improving the productivity of chickens. Farmers have discovered that the more domestic chickens peck at objects placed in their environment, the healthier and more productive the chickens seem to be.
Petroleum waste contamination. Accidental spillage and misguided disposal of petroleum wastes have resulted in extensive contamination of soils across the country. A common hazardous compound found
IRS answers to gift tax questions. According to estimates made by the General Accounting Office, the Internal Revenue Service (IRS) answered 18.3 million telephone inquiries during a recent tax
The Age Discrimination in Employment Act (ADEA) made it 1025 illegal to discriminate against workers 40 years of age and older. Opponents of the law argue that there are sound economic reasons why
The National Institute for Standards and Technology (NIST) mandates that for every 100 items scanned through the electronic checkout scanner at a retail store, no more than 2 should have an
The relationship between an employee's participation in the performance appraisal process and subsequent subordinate reactions toward the appraisal was investigated in the Journal of Applied
The primary determinant of the amount of vacation time U.S. employees receive is their length of service. According to data released by Hewitt Associates, more than 8 of 10 employers provide 2 weeks
Recently, a case of salmonella (bacterial) poisoning was traced to a particular brand of ice cream bar, and the manufacturer removed the bars from the market. Despite this response, many consumers
Suppose it is now 1 year I after the outbreak of food poisoning was traced to ice cream bars. The manufacturer wishes to estimate the proportion who still will not purchase bars to within .02 using I
In addition to the 46 hospital employees who were diagnosed with a latex allergy based on a skin-prick test, another 37 health care workers were diagnosed with the allergy using a latex-specific
When a poll reports, for example, that 61% of the public supports a program of national health insurance, it usually also reports the sampling error. For example, a poll might report that the
Each year, Management Accounting reports the results of a salary survey of the members of the Institute of Management Accountants (IMA). One year, the 2,112 members responding had a salary
A firm's president, vice presidents, department managers, and others use financial data generated by the firm's accounting system to help them make decisions regarding such things as pricing,
When companies employ control charts to monitor the quality of their products, a series of small samples is typically used to determine if the process is "in control" during the period of time in
For each of the following combinations of a and degrees of freedom (df), find the values of x2a/2 and x2(1-a/2) that would be used to form a confidence interval for σ2. For Information: use Table IV
Refer to Exercise 6.93. For each part, a-d, form a 90% confidence interval for σ. In Exercise 6.93 Given the following values of , s, and n, form a 90% confidence interval for σ2. a. = 21, s =
A random sample of n = 6 observations from a nor-Q> mal distribution resulted in the data shown in the table. Compute a 95% confidence interval for Ïƒ2.
Recall that the facial width-to-height ratio (WHR) was determined by computer analysis for each in a sample of 55 CEOs at publicly traded Fortune 500 firms, with the following results: = 1.96, s =
Recall that the level of support for corporate sustainability (measured on a quantitative scale ranging from 0 to 160 points) was obtained for each in a sample of 992 senior managers at CPA firms.
Refer to the Radiation Protection Dosimetry (December 2010) study of radon exposure in tombs carved from limestone in the Egyptian Valley of Kings, Exercise 6.30. The radon levels in the inner
The Professional Golf WH Association (PGA) and Golf Digest have developed the Play Golf America program, in which teaching professionals at participating golf clubs provide a free 10-minute lesson to
a. Find β for each of the following values of the population mean: 74,72,70,68, and 66. b. Plot each value of B you obtained in part a against its associated population mean. Show B on the vertical
Suppose you want to conduct the two tailed test of H0: p ≠ .7 against Ha: p ≠ .7 using α = .05. A random sample of size 100 will be drawn from the population in question. a. Describe the
The average size CE3 of single-family homes built in the United States is 2,390 square feet (Statistical Abstract of the United States, 2011). A random sample of 100 new homes sold in California
If a manufacturer (the vendee) buys all items of a particular type from a particular vendor, the manufacturer is practicing sole sourcing (Schonberger and Knod, Operations Management, 2001). As part
Recall that an NAB spokesperson claims that 80% of all satellite radio subscribers have a satellite radio receiver in their car. You conducted a test to determine if the claimed value is too high
You tested the null hypothesis of p = .5 against the two-tailed alternative hypothesis of p ≠ .5 using α = .01, where p represents the true proportion of blind folded students who correctly
According to the Environmental Protection Agency (EPA) Fuel Economy Guide, the 2011 Honda Civic automobile obtains a mean of 36 miles per gallon (mpg) on the highway. Suppose Honda claims that the
The performance of a particular type of laser-based inspection equipment was investigated. Assume that the standard deviation of the number of solder joints inspected on each run is 1.2. If α = .05
Specify the differences between a large-sample and small-sample test of hypothesis about a population mean p. Focus on the assumptions and test statistics.
Complete the following statement: The smaller the p-value associated with a test of hypothesis, the stronger the support for the hypothesis. Explain your answer.
The national student loan default EEI rate has fluctuated over the last several years. A few years ago, the Department of Education reported the default rate (i.e., the proportion of college students
If you select a very small value for α when conducting a hypothesis test, will β tend to be big or small? Explain.
If the rejection of the null hypothesis of a particular test would cause your firm to go out of business, would you p want a to be small or large? Explain.
A random sample of 20 observations selected from a normal population produced = 72.6 and s2 = 19.4. a. Test H0: µ = 80 against Ha: µ < 80. Use α = .05. b. Test H0: µ = 80 against Ha: µ ≠ 80.
A random sample of 175 measurements possessed a mean = 8.2 and a standard deviation s = .79. a. Test H0. µ = 8.3 against Ha: µ ≠ 8.3. Use α = .05. b. Test H0: µ = 8.4 against Ha: µ ≠ 8.4.
A random sample of n 200 observations from a binomial population yields p̂ = .29. a. Test H0: p = .35 against Ha: p < .35. Use α = .05. b. Test H0: p = .35 against Ha: p ≠ .35. Use α = .05.
A t-test is conducted for the null hypothesis H0: µ = 10 versus the alternative Ha: µ > 10 for a random sample of n = 17 observations. The test results are t = 1.174, p-value = .1288.a.
A random sample of 41 observations from a normal population possessed a mean p̂ = 88 and a standard deviation s = 6.9. a. Test H0: σ2 = 30 against Ha: σ2 > 30. Use α = .05. b. Test H0: σ2 = 30
The number of latex gloves used per week by the sampled workers is summarized as follows: x = 19.3 and s = 11.9. Let p represent the mean number of latex gloves used per week by all hospital
Let σ2 represent the variance in the number of latex gloves used per week by all hospital employees. Consider testing H0: σ2 = 100 against Ha: σ2 ≠ 100. a. Give the rejection region for the test
Work travel policy. American Express Consulting reported in USA Today (June 15, 2001) that 80% of U.S. companies have formal, written travel and entertainment policies for their employees. Give the
Recall that 64 of 106 randomly selected shoppers believed "Made in the USA" means 100% of labor and materials are from the United States. Let p represent the true proportion of consumers who believe
The "beta coefficient" of a stock is a measure of the stock's volatility (or risk) relative to the market as a whole. Stocks with beta coefficients greater than 1 generally bear greater risk (more
Recall that the National Institute for Standards and Technology (NIST) mandates that for every 100 items scanned through the electronic checkout scanner at a retail store, no more than two should
The purpose of this exercise is to compare the variability of 1 and 2 with the variability of (1 - 2). a. Suppose the first sample is selected from a population with mean µ = 150 and variance
Independent random samples from approximately normal $ populations produced the results shown below.a. Do the data provide sufficient evidence to conclude that (µ2 - µ1) > 10? Test using Î± =
A manufacturer of automobile shock absorbers was interested in comparing the durability of its shocks with that of the shocks produced by its biggest competitor. To make the comparison, one of the
Movie actors who win an Oscar usually can command a greater fee for their next motion picture. Does winning an Academy of Motion Picture Arts and Sciences award (aka, an Oscar) lead to long-term
Two quantitative variables in the data set are number of carats and selling price. One of the qualitative variables is the independent certification body.For Information: Refer to the data for 308
The 1,600 sampled viewers described their motivation for watching cable TV shopping networks by giving their level of agreement (on a 5-point scale, where 1 = strongly disagree and 5 = strongly
In evaluating the usefulness and validity of a questionnaire, researchers often pretest the questionnaire on different independently selected samples of respondents. Knowledge of the differences and
Who is more likely to get a routine medical checkup-employed or unemployed people? To answer this question, a team of physicians and public health professors collected data on a sample of over 2,200
High job turnover rates are often associated with high product defect rates because high turnover rates mean more inexperienced workers who are unfamiliar with the company's product lines (Stevenson,
The role of the cell phone in modern life was investigated by a Pew Internet & American Life Project (April 2006) survey. A total of 1,286 cell phone users were interviewed in the sample. One of the
Advertising companies often try to characterize the average user of a client's product so ads can be targeted at particular segments of the buying community. A new movie is about to be released, and
Marketing strategists would like to predict consumer response to new products and their accompanying promotional schemes. Consequently, studies that examine the differences between buyers and non
Independent random samples selected from two normal populations produced the sample means and standard deviations shown below.a. Conduct the test H0: (µ2 - µ1) = 0 against Ha: (µ2 -
A University of South Florida biologist conducted an experiment to determine whether increased levels of carbon dioxide kill leaf-eating moths (USF Magazine, Winter 1999). Moth larvae were placed in
Racial profiling is a term used to describe any police action that relies on ethnicity rather than behavior to target suspects engaged in criminal activities. Does the Los Angeles Police Department
The data on average math SAT scores for each of the 50 states and District of Columbia for the years 2001 and 2011. The data are saved in the file. (The first five observations and last two
Poisons are used to prevent rat damage in sugarcane fields. The U.S. Department of Agriculture is investigating whether the rat poison should be located in the middle of the field or on the outer
When new instruments are developed to perform chemical analyses of products (food, medicine, etc.), they are usually evaluated with respect to two criteria: accuracy and precision. Accuracy refers to
Computer-mediated communication (CMC) is a form of interaction CMC that heavily involves technology (e.g., instant messaging, e-mail). A study was conducted to compare relational intimacy in people
The researchers also hypothesized that the mean relational intimacy score for participants in the CMC group would significantly increase between the first and third meetings, but the difference
To improve quality, productivity, and timeliness, many American industries employ self-managed work teams (SMWTs). A team typically consists of 5 to 15 workers who are collectively responsible for
How does gender affect the type of advertising that proves to be most effective? An article in the Journal of Advertising Research (May/June 1990) makes reference to numerous studies that conclude
A National Adult Literacy Survey revealed that males with a postgraduate degree had a sample mean salary of $61,340 (with standard error SM = $2,185), while females with a postgraduate degree had a
With the rapid growth in legalized gambling in the United States, there is concern that the involvement of youth in gambling activities is also increasing. University of Minnesota Professor Randy
CareerBank.com conducts an annual salary survey of accounting, finance, and banking professionals. For one survey, data were collected for 2,800 responses submitted online by professionals across the
Facility layout and material flowpath design are major factors in the productivity analysis of automated manufacturing systems. Facility layout is concerned with the location arrangement of machines
Educational software-ranging from video-game-like programs played on Sony PlayStations to rigorous drilling exercises used on computers-has become very popular in school districts across the country.
Marketing professors at Robert Morris and Kent State Universities examined children's recall and recognition of television advertisements (Journal of Advertising, Spring 2006). Two groups of children
The Analytical Chemistry (Dec. 15, 2009) study in which HPLC scientists used high-performance liquid chromatography to determine the amount of drug in a tablet. Twenty-five tablets were produced at
Recall that data were collected on 3,526 forecasts made by buy-side analysts and 58,562 forecasts made by sell-side analysts, and the relative absolute forecast error was determined for each. The
How much assistance should accounting professors provide students for completing homework? Is too much assistance counterproductive? These were some of the questions of interest in a Journal of
Chance (Fall 2002) described a lawsuit where Intel Corp. was charged with infringing on a patent for an invention used in the automatic manufacture of computer chips. In response, Intel accused the
Let and 2 denote the two sample means.a. Give the mean and standard deviation of the sampling distribution of . b. Give the mean and standard deviation of the sampling distribution of 2. c. Suppose
The conversion of biomass to energy is critical for producing transportation fuels. How willing are producers to supply biomass products such as cereal straw, corn Stover, and surplus hay? To answer
Does rudeness really matter in the workplace? Studies O have established that rudeness in the workplace can lead RUDE to retaliatory and counterproductive behavior. However, there has been little
"Service with a smile" is a slogan that many businesses adhere to. However, there are some jobs (e.g., those of judges, law enforcement officers, pollsters) that require neutrality when dealing with
Refer to the Journal of Engineering for Gas Turbines and Power (Jan. 2005) study of gas turbines augmented with high-pressure inlet fogging. Exercise 7.40. The researchers classified gas turbines
Is self-employment for immigrant workers a faster route to economic advancement in the country? This was one of the questions studied in research published in the International Journal of Manpower
A paired difference experiment produced the following results: nd = 38 1 = 92 2 = 95.5 = -3.5 s2d = 21 a. Determine the values of z for which the null hypothesis, µ1 - µ2 < 0, would be rejected
A paired difference experiment yielded nd pairs of observations. In each case, what is the rejection region for testing H0: µd > 2? a. nd(t = 12, α - .05 b. nd = 24, α = .10 c. nd = 4, α =
The data for a random sample of six paired observations are shown in the next table.a. Calculate the difference between each pair of observations by subtracting observation 2 from observation 1. Use

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