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mathematics
statistics

Questions and Answers of Statistics

It is important for women to gain the right amount of weight during pregnancy by eating a healthy, balanced diet (webmd.com). It is recommended that a woman of average weight before pregnancy should
A farmer is concerned that a change in fertilizer to an organic variant might change his crop yield. He subdivides 6 lots and uses the old fertilizer on one-half of each lot and the new fertilizer on
The accompanying table shows annual return data from 2001â€“2009 for Vanguardâ€™s Balanced Index and European Stock Index mutual funds. The data set, labeled Balanced_European, can also be
The SAT is required of most students applying for college admission in the United States. This standardized test has gone through many revisions over the years. In 2005, a new writing section was
An engineer wants to determine the effectiveness of a safety program. He collects annual loss of hours due to accidents in 12 plants â€œbefore and afterâ€ the program was put into operation.
A government agency wants to determine whether the average salaries of four various kinds of transportation operators differ. A random sample of five employees in each of the four categories yields
An economist wants to determine whether average Price/Earnings (P/E) ratios differ for firms in three industries. Independent samples of five firms in each industry show the following results:a.
The manager of an SAT review program wonders whether average SAT scores differ depending on the ethnicity of the test taker. Thirty test scores for four ethnicities are collected. A portion of the
An engineer wants to determine whether the average strength of plywood boards (in pounds per square inch) differs depending on the type of glue used.For three types of glue, she measures the strength
Consider the following competing hypotheses and accompanying results from matched samples:H0: µD ≤ 2; HA: µD > 2d̅ = 5.6 , sD = 6.2 , n = 10a. Calculate the value of the test statistic and
The following Excel output summarizes the results of an analysis of variance experiment in which the treatments were three different hybrid cars and the variable measured was the miles per gallon
An employee of a small software company in Minneapolis bikes to work during the summer months. He can travel to work using one of three routes and wonders whether the average commute times (in
Before the recession, job-creating cities in the Sunbelt, likeÂ Las Vegas, Phoenix, and Orlando, saw their populations, income levels, and housing prices surge. Las Vegas, however, offered
David Anderson has been working as a lecturer at Michigan State University for the last three years. He teaches two large sections of introductory accounting every semester. While he uses the same
A statistics instructor wonders whether significant differences exist in her studentsâ€™ final exam scores in her three different sections. She randomly selects the scores from 10 different
An accounting professor wants to know if students perform the same on the departmental final exam irrespective of the accounting section they attend. For three sections, he obtains the final exam
Chad Perrone is a financial analyst in Boston studying the annual return data for the health and information technology industries. He randomly samples 20 firms in each industry and notes each
The Speedo LZR Racer Suit is a high-end, body-length swimsuit that was launched onFebruary 13, 2008. When 17 world records fell at the December 2008 European Short CourseChampionships in Croatia,
Lisa Grattan, a financial analyst for a small investment firm, collects annual stock return data for 10 firms in the energy industry, 13 firms in the retail industry, and 16 firms in the utilities
Given x1 = 50, n1 = 200, x2 = 70, n2 = 250, construct a 95% confidence interval for the difference between the population proportions. Is there a difference between the population proportions at the
Given = 0.85, n1 = 400, = 0.90, n2 = 350, construct a 90% confidence interval for the difference between the population proportions. Is there a difference between the population proportions at
Consider the following competing hypotheses and accompanying sample data.H0: - = 0HA: - ≠ 0x1 = 100 x2 = 172n1 = 250 n2 = 400a. Calculate the value of the test statistic.b. Calculate the
Consider the following competing hypotheses and accompanying sample data.a. At the 5% significance level, find the critical value(s).b. Calculate the value of the test statistic.c. What is the
Consider the following competing hypotheses and accompanying sample data.H0: - = 0HA: - ≠ 0x1 = 300 x2 = 325n1 = 600 n2 = 500a. Calculate the value of the test statistic.b. Calculate the
Consider the following competing hypotheses and accompanying sample data.a. Calculate the value of the test statistic.b. Calculate the p-value.c. At the 5% significance level, what it the conclusion
A recent study claims that girls and boys do not do equally well on math tests taken from the 2nd to 11th grades (Chicago Tribune, July 25, 2008). Suppose in a representative sample, 344 of 430 girls
According to the Pew report, 14.6% of newly married couples in 2008 reported that their spouse was of another race or ethnicity (CNNLiving, June 7, 2010). In a similar survey in 1980, only 6.8% of
Research by Harvard Medical School experts suggests that boys are more likely than girls to grow out of childhood asthma when they hit their teenage years (BBC News, August 15, 2008). Scientists
More people are using social media to network, rather than phone calls or e-mails (US News & World Report, October 20, 2010). From an employment perspective, jobseekers are no longer calling up
According to a recent report, 32.2% of American adults (aged 20 and older) are obese (New York Times, August 15, 2008).Among ethnic groups in general, African-American women are more overweight than
Only 26% of psychology majors are “satisfied” or “very satisfied” with their career paths as compared to 50% of accounting majors (The Wall Street Journal, October 11, 2010).Suppose these
A recent report suggests that business majors spend the least amount on course work than all other college students (New York Times, November 17, 2011). A provost of a university decides to conduct a
Consider a multinomial experiment with n = 250 and k = 4.The null hypothesis to be tested is H0: p1 = p2 = p3 = p4 = 0.25.The observed frequencies resulting from the experiment area. Specify the
Consider a multinomial experiment with n = 400 and k = 3.The null hypothesis is H0: p1 = 0.60, p2 = 0.25 and p3 = 0.15.The observed frequencies resulting from the experiment area. Deine the
A multinomial experiment produced the following results:Can we conclude at the 1% significance level that the population proportions are notequal?
A multinomial experiment produced the following results:At the 1% significance level, can we reject H0: p1 = 0.30, p2 = 0.20 and p3 =0.50?
You suspect that an unscrupulous employee at a casino has tampered with a die; that is, he is using a loaded die. In order to test this claim, you roll the die 200 times and obtain the following
A study conducted in September and October of 2010 found that fewer than half of employers who hired new college graduates last academic year plan to definitely do so again (The Wall Street Journal,
A rent-to-own (RTO) agreement appeals to low-income and financially distressed consumers. It allows immediate access to merchandise, and by making all payments, the consumer acquires the merchandise.
Despite Zimbabwe’s shattered economy, with endemic poverty and widespread political strife and repression, thousands of people from overseas still head there every year (BBC News,August 27, 2008).
In 2003 The World Wealth Report first started publishing market shares of global millionaires (The Wall Street Journal, June 25, 2008). At this time, the distribution of the world’s people worth $1
An Associated Press/GfK Poll shows that 38% of American drivers favor U.S. cars, while 33% prefer Asian brands, with the remaining 29% going for other foreign cars (www.msnbc.com, April 21, 2010).
Given the following contingency table, conduct a test of independence at the 5% significance level using(a) The critical value approach and(b) The p-valueapproach.
Given the following contingency table, conduct a test of independence at the 1% significance level using(a) The p -value approach and(b) The critical valueapproach.
According to an online survey by Harris Interactive for job site CareerBuilder.com (InformationWeek.com, September 27, 2007), more than half of IT workers say they have fallen asleep at work.
A market researcher for an automobile company suspects differences in preferred color between male and female buyers. Advertisements targeted to different groups should take such differences into
The following sample data reflect shipments received by a large firm from three different vendors.a. Specify the competing hypotheses to determine whether quality is associated with the source of the
According to a 2008 survey by the Pew Research Center, people in China are highly satisfied with their roaring economy and the direction of their nation (USA TODAY, July 22, 2008). Eighty-six percent
A study by the Massachusetts Community & Banking Council found that blacks, and, to a lesser extent, Latinos, remain largely unable to borrow money at the same interest rate as whites (Boston Globe,
Founded in February 2004, Facebook is a social utility that helps people communicate with their friends and family. In just six years, Facebook has acquired more than 500 million active users, of
A recent Health of Boston report suggests that 14% of female residents suffer from asthma as opposed to 6% of males (Boston Globe, August 16, 2010). Suppose 250 females and 200 males responded to the
Depression engulfs millions of Americans every day. A new federal study reported that 10.9% of adults aged 18–24 identified with some level of depression versus 6.8% of adults aged 65 or older
Fresh numbers from the U.S. Department of Transportation suggest that fewer lights in the U.S. arrive on time than before. The explanations offered for the lackluster performance are understaffed
The following table lists the market share of the four firms in a particular industry in 2010 and total sales for each firm in 2011.a. Specify the competing hypotheses to test whether the market
A study suggests that airlines have increased restrictions on cheap fares by raising overnight requirements (The Wall Street Journal, August 19, 2008). This would force business
A local TV station claims that 60% of people support Candidate A, 30% support Candidate B, and 10% support Candidate C. A survey of 500 registered voters is taken. The accompanying table indicates
Although founded only in 2004, Facebook has more than 500 million active users, of which 50% log on to Facebook on any given day. In a recent survey by Facebook, young users (those born after 1984)
A recent study in the Journal of the American Medical Association (February 20, 2008) found that patients who go into cardiac arrest while in the hospital are more likely to die if it happens after
An analyst is trying to determine whether the prices of certain stocks on the NASDAQ are independent of the industry to which they belong. She examines four industries and classifies the stock prices
Many parents have turned to St. Johnâ€™s Wort, a herbal remedy, to treat their children with attention deficit hyperactivity disorder (ADHD). The Journal of the American Medical Association
A recent poll asked 3,228 Americans aged 16 to 21 whether they are likely to serve in the U.S. military. The following table, cross-classified by gender and race, reports those who responded that
Given a shaky economy and high heating costs, more and more households are struggling to pay utility bills (The Wall Street Journal, February, 14, 2008). Particularly hard hit are households with
According to the Census’s Population Survey, the percentage of children with two parents at home is the highest for Asians and lowest for blacks (USA TODAY, February 26, 2009). It is reported that
Suppose you are conducting a test of independence. Specify the critical value under the following scenarios:a. r = 3, c = 3, and α = 0.10 .b. r = 4, c = 5, and α = 0.05 .
Suppose you are conducting a test of independence. Specify the critical value under the following scenarios:a. r = 5, c = 2, and α = 0.025 .b. r = 3, c = 5, and α = 0.01 .
It has generally been believed that it is not feasible for men and women to be just friends (New York Times, April 12, 2012). Others argue that this belief may not be true anymore since gone are the
According to a recent study, cell phones are the main medium for teenagers to stay connected with friends and family (CNN, March 19, 2012). These days text messaging followed by cell calling have
A detailed study of Americansâ€™ religious beliefs and practices by the Pew Forum on Religion & Public Life revealed that religion is quite important in an individualâ€™s life (Boston
A University of Utah study examined 7,925 severely obese adults who had gastric bypass surgery and an identical number of people who did not have the surgery (Boston Globe, August 23, 2007). The
A sample space S yields five equally likely events, A, B, C, D, and E.a. Find P(D) .b. Find P(Bc) .c. Find P(A ∪ C ∪ E) .
You roll a die with the sample space S = {1, 2, 3, 4, 5, 6}. You define A as {1, 2, 3}, B as {1, 2, 3, 5, 6}, C as {4, 6}, and D as {4, 5, 6}. Determine which of the following events are exhaustive
A sample space, S, yields four simple events, A, B, C, and D, such that P(A) = 0.35 , P(B) = 0.10 and P(C) = 0.25.a. Find P(D).b. Find P(Cc).c. Find P(A ∪ B).
An alarming number of U.S. adults are either overweight or obese. The distinction between overweight and obese is made on the basis of body mass index (BMI), expressed as weight/height2. An adult is
Many communities are finding it more and more difficult to ill municipal positions such as town administrators, finance directors, and treasurers. The following table shows the percentage of
At four community health centers on Cape Cod, Massachusetts, 15,164 patients were asked to respond to questions designed to detect depression (The Boston Globe, June 11, 2008). The survey produced
Let P (A) = 0.65, P(B) = 0.30, and P(A | B) = 0.45.a. Calculate P (A ∩ B).b. Calculate P (A ∪ B).c. Calculate P (B | A).
Let P (A) = 0.55, P (B) = 0.30, and P (A ∩ B) = 0.10.a. Calculate P (A | B).b. Calculate P (A ∪ B).c. Calculate P ((A ∪ B)c).
Let A and B be mutually exclusive with P (A) = 0.25 and P (B) = 0.30.a. Calculate P (A ∩ B).b. Calculate P (A ∪ B).c. Calculate P (A | B).
Let A and B be independent with P (A) = 0.40 and P (B) = 0.50.a. Calculate P (A ∩ B).b. Calculate P ((A ∪ B)c).c. Calculate P (A | B).
Let P (A) = 0.65, P (B) = 0.30, and P (A | B) = 0.45.a. Are A and B independent events? Explain.b. Are A and B mutually exclusive events? Explain.c. What is the probability that neither A nor B takes
Let P (A) = 0.15, P (B) = 0.10, and P (A ∩ B) = 0.05.a. Are A and B independent events? Explain.b. Are A and B mutually exclusive events? Explain.c. What is the probability that neither A nor B
Consider the following probabilities: P(A) = 0.25, P(B c) = 0.40, and P(A ∩ B) = 0.08. Find:a. P(B)b. P(A | B)c. P(B | A)
Consider the following probabilities: P (Ac) = 0.30, P (B) = 0.60, and P (A ∩ Bc) = 0.24. Find:a. P (A | Bc)b. P (Bc | A)c. Are A and B independent events? Explain.
Consider the following probabilities: P (A) = 0.40, P (B) = 0.50 and P (Ac ∩ Bc) = 0.24. Find:a. P (Ac | Bc)b. P (Ac ∪ Bc)c. P (A ∪ B)
Survey data, based on 65,000 mobile phone subscribers, shows that 44% of the subscribers use smart-phones (Forbes, December 15, 2011). Moreover, 51% of smart-phone users are women.a. Find the
Twenty percent of students in a college ever go to their professor during office hours. Of those who go, 30% seek minor clarification and 70% seek major clarification.a. What is the probability that
The probabilities that stock A will rise in price is 0.40 and that stock B will rise in price is 0.60. Further, if stock B rises in price, the probability that stock A will also rise in price is
Despite government bailouts and stimulus money, unemployment in the United States had not decreased significantly as economists had expected (US News and World Report, July 2, 2010). Many analysts
Dr. Miriam Johnson has been teaching accounting for over 20 years. From her experience she knows that 60% of her students do homework regularly. Moreover, 95% of the students who do their homework
Records show that 5% of all college students are foreign students who also smoke. It is also known that 50% of all foreign college students smoke. What percent of the students at this university are
An analyst estimates that the probability of default on a seven-year AA-rated bond is 0.06, while that on a seven-year A-rated bond is 0.13. The probability that they will both default is 0.04.a.
In general, shopping online is supposed to be more convenient than going to stores. However, according to a recent Harris Interactive poll, 87% of people have experienced problems with an online
Mike Danes has been delayed in going to the annual sales event at one of his favorite apparel stores. His friend has just texted him that there are only 20 shirts left, of which 8 are in size M, 10
A manufacturing firm just received a shipment of 20 assembly parts, of slightly varied sizes, from a vendor. The manager knows that there are only 15 parts in the shipment that would be suitable. He
Despite the repeated effort by the government to reform how Wall Street pays its executives, some of the nation’s biggest banks are continuing to pay out bonuses nearly as large as those in the
Apple products have become a household name in America with 51 percent of all households owning at least one Apple product (CNN, March 19, 2012). The likelihood of owning an Apple product is 61
According to the Census’s Population Survey, the percentage of children with two parents at home is the highest for Asians and lowest for blacks (USA TODAY, February 26, 2009). It is reported that
Christine Wong has asked Dave and Mike to help her move into a new apartment on Sunday morning. She has asked them both in case one of them does not show up. From past experience, Christine knows
According to a recent survey by two United Nations agencies and a nongovernmental organization, two in every three women in the Indian capital of New Delhi are likely to face some form of sexual
Since the fall of 2008, millions of Americans have lost jobs due to the economic meltdown. A recent study shows that unemployment has not impacted white-collar and blue-collar workers equally

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