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mathematics
statistics

Questions and Answers of Statistics

The data for a random sample of 10 paired observations are shown in the table below.a. If you wish to test whether these data are sufficient to indicate that the mean for population 2 is larger than
In order to compare the means of two populations, inde-CE1 pendent random samples of 400 observations are selected from each population, with the following results:a. Use a 95% confidence interval to
A paired difference experiment yielded the following results: nd = 40 ∑d = 468 ∑d2 = 6,880 a. Test H0: µd = 10 against Ha: µd ≠ 10, where µd = (µ1 - µ2). Use α = .05. b. Report the
Camp Jump Start is an 8-week summer camp for overweight and obese adolescents. Counselors develop a weight-management program for each camper that centers on nutrition education and physical
The U.S. Office of Management and Budget (OMB) requires government agencies to produce annual performance and accounting reports (PARS) each year. A research team at George Mason University evaluated
A traditional method of verifying mineralization grades in mining is to drill twinned holes. i.e., the drilling of a new hole, or "twin," next to an earlier drill hole. The use of twinned drill holes
Recall that a fictitious brand of a healthy food product- sliced apples-was packaged to appeal to children (a smiling cartoon apple was on the front of the package). The researchers compared the
To improve response rates in telephone surveys, interviewers are often instructed by the polling company to state, "I am not selling anything" at the outset of the call. The effectiveness of the "I
The National 9 Highway Traffic Safety Administration (NHTSA) crash-test data for new cars saved in the file. Crash-test dummies were placed in the driver's seat and front passenger's seat of a new
Lack of sleep costs companies about $18 billion a year in lost productivity, according to the National Sleep Foundation. Companies are waking up to the problem, however. Some even have quiet rooms
Acid has been found to be a primary cause of dental caries (cavities). It is theorized that oral mouthwashes contribute to the development of caries due to the antiseptic agent oxidizing into acid
Japanese researchers have developed a compression/depression method of testing electronic circuits based on Huffman coding (IEICE EEI Transactions on Information & Systems, Jan. 2005). The new method
To use the t-statistic to test for a difference between the means of two populations, what assumptions must be made about the two populations? About the two samples? Discuss.
To combat & red-light-running crashes-the phenomenon of a motorist entering an intersection after the traffic signal turns red and causing a crash-many states are adopting photo-red enforcement
Merck Research Labs conducted $ an experiment to evaluate the effect of a new drug using the single-T swim maze. Nineteen impregnated dam rats were captured and allocated a dosage of 12.5 milligrams
Determining alcoholic fermentation in wine is critical to the wine-making process. Must/wine density is a good indicator of the fermentation point because the density value decreases as sugars are
Consider making an inference about p1 - p2, where there are x1 successes in n1 binomial trials and x2 successes in n2 binomial trials. a. Describe the distributions of x1 and x2. b. Explain why the
For each of the following values of a, find the values of z for which H0: (p1 - p2) = 0 would be rejected in favor of Ha: (p1 - P2) < 0. a. α = .01 b. α = .025 c. α = .05 d. α = .10
In each case, determine whether the sample sizes are large enough to conclude that the sampling distribution of (p̂1 - p̂2) is approximately normal.a. n1 = 12, n2 = 14, p̂1, = .42, p̂2 - .57b. n1
Construct a 95% confidence interval for (p1 - p2) in each of the following situations:a. n1 = 400, p̂1, = .65; n2 = 400, p̂2 = .58b. n1 = 180, p̂1, = .31; n2 = 250, p̂2 = .25c. n1 = 100, p̂1, =
Independent random samples, each containing 800 observations, were selected from two binomial populations. The samples from populations 1 and 2 produced 320 and 400 successes, respectively. a. Test
Random samples of size n1 = 55 and n2 - 65 were drawn from populations 1 and 2, respectively. The samples yielded p̂1 = .7 and p̂2 = .6. Test H0: (p1 - p2) = 0 against Ha: (P1 - P2) > 0 using a =
In auction bid-ding, the "winner's curse" is the phenomenon of the winning (or highest) bid price being above the expected value of the item being auctioned. The Review of Economics and Statistics
Recall that independent samples of Missouri producers and Illinois producers were surveyed. Another aspect of the study focused on the services producers were willing to supply. One key service
One of the most serious health problems in India is malaria. Consequently, Indian hospital administrators must have the resources to treat the high volume of malaria patients that are admitted.
The rapid evolution of computer hardware and software has made it easy for businesses to conduct computer-based and Web-based (i.e., electronic) surveys. Professors at Michigan State and DePaul
Salmonella is the most common type of bacterial food-borne illness in the United States. How prevalent is salmonella in produce grown in the major agricultural region of Monterey, California?
Are African American MBA students more likely to begin their careers as entrepreneurs than white MBA students? This was a question of interest to the Graduate Management Admission Council (GMAC).
Refer to the PROMISE Software Engineering Repository data on 498 modules of software code written in "C" language for a NASA spacecraft instrument, saved in the file. (See Exercise 3.76, p. 168)
Do you have an insatiable craving for chocolate or some other food? Because many North Americans apparently do, psychologists are designing scientific studies to examine the phenomenon. According to
Assume that σ21 = σ22 = σ21. Calculate the pooled estimator of σ2 for each of the following cases: a. s21 = 120, s22 = 100, n1 = n2 = 25 b. s2 = 12, s22 = 20, n1, = 20, n2 = 10 c. s2 = .15, s22 =
Assuming that n1 - n2, find the sample sizes needed to estimate (p1 - p2) for each of the following situations: a. Margin of error = .01 with 99% confidence. Assume that p1 ≈ .4 and p2 ≈ .7. b. A
Find the appropriate values of n1 and n2 (assume n1 = n2) needed to estimate (µ1 - µ2) for each of the following situations: a. A margin of error equal to 3.2 with 95% confidence. From prior
Suppose you want to estimate the difference between two populations means correct to within 1.8 with a 95% confidence interval. If prior information suggests that the population variances are
Recall that the mean response times (in minutes) to acquire basketball tickets were compared for two groups of MBA students -those students with last names beginning with one of the first nine
Recall that one group of students was given a completed homework solution and another group was given only check figures at various steps of the solution. The researchers wanted to compare the
Decision Lint (July 2001) study designed to compare the response rates of electronic surveys and traditional print surveys, Exercise 8.54. Recall that the two surveys were developed for customers who
A pollster wants to estimate the difference between the proportions of men and women who favor a particular national candidate using a 90% confidence interval of width .04. Suppose the pollster has
Is housework hazardous to your health? A study in Public Health Reports compared the life expectancies of 25-year-old white women in the labor force to those who are housewives. How large a sample
Independent random samples from normal populations produced the results shown in the next table. Sample 1 Sample
All cable companies carry at least one home shopping channel. Who uses these home shopping services? Are the shoppers primarily men or women? Suppose you want to estimate the difference in the
Recall that half the patients were randomly assigned to get an angioplasty and half were not. The researchers compared the proportion of patients with subsequent heart attacks for the two groups and
Even though Japan is an economic superpower, Japanese workers are in many ways worse off than their U.S. and European counterparts. For example, the estimated average housing space per person (in
Use Tables V, VI, VII, and VIII in Appendix D to find each of the following F-values: a. F.05 where v1 = 9 and v2 = 6 b. F.05 where v1 = 18 and v2 = 14 c. F.05 where v1 = 11 and v2 - 4 d. F.05 where
Given v1, and v2, find the following probabilitiesa. v1 = 2, v2 = 30, P(F > 5.39)b. v1 = 24, v2 = 10, P(F < 2.74)c. v1 = 7, v2 = 1, P(F < 236.8)d. v1 = 40, v2 = 40, P(F > 2.11)
For each of the following cases, identify the rejection region that should be used to test H0: σ21 = σ22 against Ha: σ21 > σ22. Assume v1 = 30 and v2 = 20. a. α = .10 b. α = .05 c. α = 025 d.
For each of the following cases, identify the rejection region that should be used to test H0: σ21 = σ22 against Ha: σ21 ≠ σ22. Assume v1 = 10 and v2 = 12.a. α = .20b. α = .10c. α = .05d. α
Specify the appropriate rejection region for testing H0: σ21 = σ22 in each of the following situations:a. Ha: σ21 > σ22; α = .05, n1, = 25, n2 = 20b. Ha: σ21 < σ22; α = .05, n1, = 10,
Independent random samples were selected from each of two normally distributed populations, n1, = 12 from population 1 and n2 = 27 from population 2. The means and variances for the two samples are
Independent random samples were selected from each of 0 two normally distributed populations, n1, = 6 from population 1 and n2 = 5 from population 2. The data are shown in the table.a. Test H0:
The data are repeated here (next column). You used the small-sample t-statistic to form a confidence interval for the difference between the mean trap-spacing measurements of the two fishing
You used a small-sample t-test to test the null hypothesis H0: (µ1 - µ2) = 0, where µ1 = mean number of ads recalled by children in the video only group and µ2 = mean number
A study in the Journal of Occupational and Organizational Psychology investigated the relationship of employment status and mental health. A sample of working and unemployed people was selected, and
Recall that 25 tablets were produced at each of two different, independent sites. The researchers want to determine if the two sites produced drug concentrations with different variances. A Minitab
The zinc measurements for three locations on the original inventor's notebook - on a text line, on a witness line, and on the intersection of the witness and text line -are reproduced in the
Tests of product quality using human inspectors can lead to serious inspection error problems (Journal of Quality Technology). To evaluate the performance of inspectors in a new company, a quality
Heat rate data (kilojoules per kilowatt per hour) for each of three types of gas turbines (advanced, aeroderivative, traditional) are saved in the accompanying file. In order to compare the mean heat
Following the initial Persian Gulf War, the Pentagon changed its logistics processes to be more corporate-like. The extravagant "just-in-case" mentality was replaced with "just-in-time" systems.
Archives of Pediatrics and Adolescent Medicine (Dec. 2007) study of honey as a children's cough remedy, Exercise 8.23. The data (cough improvement scores) for the 33 children in the DM dosage group
Independent random samples of n1 = 233 and n2 = 312 are selected from two populations and used to test the hypothesis H0: (µ1 - µ2) = 0 against the alternative Ha: (µ1 - µ2) ≠ 0. a. The
Independent random samples were selected from two binomial populations. The sizes and number of observed successes for each sample are shown in the following table. Sample 1 Sample
Two independent random samples are taken from two populations. The results of these samples are summarized in the next table.a. Form a 90% confidence interval for (µ1 - µ2). b. Test H0:
A study reported in Inside Higher Education News (May 22, 2006) found that financial incentives can improve low-income college students' grades and retention. As part of their "Opening Doors"
A study published in The Journal of American Academy of Business, Cambridge (March 2002) examined whether the perception of service quality at five-star hotels in Jamaica differed by gender. Hotel
The data for the 42 recent spills are saved in the accompanying file.a. Construct a 90% confidence interval for the difference between the mean spillage amount of accidents caused by collision and
Do students who play virtual-reality educational software games perform better in school? If so, software designers will use this information to create more attractive and motivating educational
Recall that 50 consumers were randomly selected from all consumers in a designated market area to participate in the study. The researchers randomly assigned 25 consumers to read a within-store price
Three anticoagulant drugs are £€¢ studied to compare their effectiveness in dissolving blood clots. Each of five subjects receives the drugs at equally spaced time intervals and in random order.
A quality-control supervisor measures the quality of a steel ingot on a scale of 0 to 10. He designs an experiment in which three different temperatures (ranging from 1,100 to 1,200 °F) and five
Advancements in information technology have yielded services that compete against products, with each providing roughly the same benefits to the consumer (e.g., home answering machines and voice-mail
Recall that the file contains information on the quantitative variables, size (number of carats) and price (in dollars), and on the qualitative variables, color (D, E, F, G, H. and I), clarity (IF.
A study was conducted to investigate the effect of prompting in a walking program instituted at a large corporation (Health Psychology, Mar. 1995). Five groups of walkers-27 in each group-agreed to
Research published in Accounting, Organizations and Society (Vol. 19, 1994) investigated whether the effects of different performance evaluation styles (PES) on the level of job-related tension is
Factorial designs are commonly employed in marketing re-SUPMKT search to evaluate the effectiveness of sales strategies. At one supermarket, two of the factors were price level (regular, reduced
Traditionally, people protect themselves from mosquito bites by applying insect repellent to their skin and clothing. Research suggests that permethrin, an insecticide with low toxicity to humans,
Qualm Engineering (Vol. 6, 1994) reported the results of an experiment that was designed to find ways to improve the output of an industrial lathe. The lathe is controlled by a computer that
In addition to the factor. Type of advertisement (within-store price promotion and between-store price promotion), the researchers also investigated the impact of a second factor-Location where ad is
The Electronic Journal of Biotechnology (Dec. 15, 2003) published an article on a comparison of two yeast extracts-baker's yeast and brewer's yeast. Brewer's yeast is a surplus by-product obtained
Paracetamol is the active ingredient in drugs designed to relieve mild to moderate pain and fever. To save costs, pharmaceutical companies are looking to produce paracetamol tablets from locally
Find each of the following F values: a. F.05, v1 = 4, v2 = 4 b. f.01, v1 = 4, v2 = 4 c. F.10 v1 = 30, v2 = 40 d. F.025 v1 = 15, v2 = 12 For Information: Use Tables V. VI, VII, and VIII in Appendix D
Find the following probabilities: a. P(F < 3.48) for v1, = 5, v2 = 9 b. P(F > 3.09) for v1, = 15, v2 = 20 c. P(F > 2.40) for v1, = 15, v2 = 15 d. P(F < 1.83) for v1, = 8, v2 = 40
Consider dot plots 1 and 2 shown below. Assume that the two samples represent independent, random samples corresponding to two treatments in a completely randomized design.a. In which plot is the
Conduct a two-sample Mest (Section 8.2) of the null hypothesis that the two treatment means are equal for each dot plot. Use α = .05 and two-tailed tests. In the course of the test, compare each of
Complete the following ANOVA table for each of the two dot plots:For Information: Refer to Exercises 9.17 and 9.18.
What are the treatments for a designed experiment with two factors, one qualitative with two levels (A and B) and one quantitative with five levels (50, 60, 70, 80, and 90)?
A partially completed ANOVA table for a completely randomized design is shown here:a. Complete the ANOVA table.b. How many treatments are involved in the experiment?c. What is the total sample size,
The data in the next table resulted from an experiment that used a completely randomized design.a. Use statistical software (or the appropriate calculation formulas in Appendix C) to complete the
A randomized field experiment was carried out to determine how workers respond to wage cuts and the results published in Institute for the Study of Labor: Discussion Paper Series (March 2011). A
The performances of public bus depots in India were evaluated and ranked in the International Journal of Engineering Science and Technology (February 2011). A survey was administered to 150 customers
The Journal of Economic Psychology (Sep. 2008) published the results of a high-stakes experiment where subjects (university students) were asked how much they would pay for insuring a valuable
Contingent valuation (CV) is a method of estimating property values that uses survey responses from potential homeowners. CV surveys were employed to determine the impact of contamination on property
Mutual funds are classified as large-cap funds, medium-cap funds, or small-cap funds, depending on the capitalization of the companies in the fund. Hawaii Pacific University researchers S. Shi and
Is a driver's propensity to engage in road rage related to his or her income? Researchers at Mississippi State University attempted to answer this question by conducting a survey of a representative
Do TV shows with violence and sex impair memory for commercials? To ADREC answer this question, Iowa State researchers conducted a designed experiment in which 324 adults were randomly assigned to
Dermatologists' primary recommendation to prevent skin cancer is minimal exposure to the sun. Yet, models used in product advertisements are typically well tanned. Do such advertisements influence a
A total of 75 junior-level accounting majors who were enrolled in Intermediate Financial Accounting participated in the experiment. Recall that students took a pretest on a topic not covered in class
Industrial sales professionals have long debated the effectiveness of various sales closing techniques. For example, a University of Akron study investigated the impact of five different closing
Pediatric researchers at $ Pennsylvania State University carried out a designed HCOUGH study to test whether a teaspoon of honey before bed calms a child's cough and published their results in
In the production of commercial eggs in Europe, four EGGS different types of housing systems for the chickens are used: cage, barn, free range, and organic. The characteristics of eggs produced from
Chief executive officers of hospitals are adopting unconventional therapeutic methods to shorten the length of stay of patients. At an American Heart Association Conference (Nov. 2005), a study to

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