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mathematics
statistics

Questions and Answers of Statistics

Consider the following competing hypotheses and relevant summary statistics:H0: ????21 ∕ ????22 = 1HA: ????21 ∕ ????22 ≠ 1Sample 1: X̅1 = 48.5, s21 = 18.7, and n1
Consider the following competing hypotheses and relevant summary statistics:H0: ????21 ∕ ????22 ≤ 1HA: ????21 ∕ ????22 > 1Sample 1: s21= 935 and n1 = 14Sample 2: s22 =
Consider the following competing hypotheses and relevant summary statistics:H0: ????21 ∕ ????22 ≥ 1HA: ????12 ∕ ????22 < 1Sample 1: s21= 1,315 and n1 = 17Sample 2:
A firm has just developed a new cost-reducing technology for producing a certain replacement part for automobiles. Since a replacement part must be produced within close specifications in order for
Two basketball players on a school team are working hard on consistency of their performance. In particular, they are hoping to bring down the variance of their scores. The coach believes that the
The following table shows the annual returns (in percent) for Fidelity's Electronic and Utilities funds.Using the critical value approach, test if the population variances differ at the 5%
Nike's total revenues (in millions of $) for the Asian and Latin American regions for the years 2005 through 2009 are as follows:a. Specify the competing hypothesis in order to test whether the
The quality manager at a battery manufacturing company wants to determine if lithium-ion batteries have less variability in discharge time than nickel-cadmium batteries. Using products with similar
A marketing analyst is studying the variability in customer purchase amounts between shopping mall stores and "big box" discount stores. She suspects the variability is different between those stores
A portion of the monthly stock prices (rounded to the nearest dollar) for Starbucks Corp. and Panera Bread Co. from 2010 to 2013 are reported in the following table.a. State the null and the
A variety of packaging solutions exist for products that must be kept within a specific temperature range. Cold chain distribution is particularly useful in the food and pharmaceutical industries. A
The data accompanying this exercise include monthly rents for a two-bedroom apartment in two campus towns: Ann Arbor, Michigan, and Davis, California. Davis, California is known to have higher rents
A replacement part for a machine must be produced within close specifications in order for it to be acceptable to customers. A production process is considered to be working properly as long as the
A random sample of 25 observations is used to estimate the population variance. The sample mean and sample standard deviation are calculated as 52.5 and 3.8, respectively. Assume that the population
A consumer advocacy group is concerned about the variability in the cost of a generic drug. There is cause for concern if the variance of the cost exceeds 5 ($)2. The group surveys seven local
A financial analyst maintains that the risk, measured by the variance, of investing in emerging markets is more than 280(%)2. Data on 20 stocks from emerging markets revealed the following sample
Fizzco, a beverage manufacturing company, is interested in determining whether the standard deviation of their dispensing process has changed from a required level of 5 milliliters. They have taken a
For staffing purposes, a retail store manager would like to standardize the number of checkout lanes to keep open on a particular shift. She believes that if the standard deviation of the hourly
The following table presents a portion of the annual returns for Fidelity's Select Automotive Fund (in percent). This mutual fund invests primarily in companies engaged in the manufacturing, the
John Daum and Chris Yin are star swimmers at a local college. They are preparing to compete at the NCAA Division II national championship meet, where they both have a good shot at earning a medal in
Annual growth rates for individual firms in the toy industry tend to fluctuate dramatically, depending on consumers' tastes and current fads. Consider the following growth rates (in percent) for two
At Burger Joint, consistency in product and service is the new motto. Accordingly, management has invested in an automated French-fry dispenser to replace the manual dispensing method. The goal is to
An automotive parts distributor wants to standardize its safety stock level for two parts, A and B. ("Safety stock" is the excess inventory carried above the expected demand level to provide
Barbara Dwyer, the manager at Lux Hotel, makes every effort to ensure that customers attempting to make phone reservations do not have to wait too long to speak with a reservation specialist. Since
The following values are drawn from a normal population. 20 29 32 27 34 25 30 31 a. Calculate the point estimates for the population variance and the population standard deviation. b. Construct the
Adidas revenues (in millions of ‚¬) in Asia and Latin America for the years 2005 through 2009 are shown in the accompanying table. Assume revenues are normally distributed.a. Specify the
In order to conduct a hypothesis test for the population variance, you compute s2 = 75 from a sample of 21 observations drawn from a normally distributed population. Use the critical value approach
Consider the following hypotheses:H0: ????2 = 200HA: ????2 ≠ 200Approximate the p-value based on the following sample information, where the sample is drawn from a normally distributed
You would like to test the claim that the variance of a normally distributed population is more than 2 squared units. You draw a random sample of 10 observations as 2, 4, 1, 3, 2, 5, 2, 6, 1, 4. At
A research analyst is examining a stock for possible inclusion in his client's portfolio. Over a 10-year period, the sample mean and the sample standard deviation of annual returns on the stock were
Due to environmental concerns and the never-ending volatility of gas prices, drivers are becoming more concerned with their cars' as oline consumption.Cameron White, a research analyst at a nonprofit
Nicholas Grammas is an investment analyst examining the performance of two mutual funds with Janus Capital Group: The Janus Balanced Fund and the Janus Overseas Fund.â€¢ The Janus Balanced Fund:
For decades, people have believed that boys are innately more capable than girls in math. In other words, due to the intrinsic differences in brains, boys are better suited for doing math than girls.
The quality department at an electronics company has noted that, historically, 92% of the units of a specific product pass a test operation, 6% fail the test but are able to be repaired, and 2% fail
An agricultural grain company processes and packages various grains purchased from farmers. A high-volume conveyor line contains four chutes at the end, each of which is designed to receive and
A marketing agency would like to determine if there is a relationship between union membership and type of vehicle owned (domestic or foreign brand). The goal is to develop targeted advertising
(Use Excel) The quality manager believes there may be a relationship between the experience level of an inspector and whether a product passes or fails inspection. Inspection records were reviewed
(Use Excel) 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).
Consider the following sample data with mean and standard deviation of 20.5 and 5.4, respectively.Class .............................. FrequencyLess than 10 ............................. 2510 up to
The following frequency distribution has a sample mean of -3.5 and a sample standard deviation of 9.7.Class ............................ FrequencyLess than -10 ....................... 70-10 up to 0
You are given the following summary statistics from a sample of 50 observations:Mean ................................ 77.25Standard Deviation ............... 11.36Skewness ...........................
An economics professor states on her syllabus that final grades will be distributed using the normal distribution. The final averages of 300 students are calculated, and she groups the data into a
Fifty cities provided information on vacancy rates (in percent) in local apartments in the following frequency distribution. The sample mean and the sample standard deviation are 9% and 3.6%,
A multinomial experiment produced the following results:Can we conclude at the 1% significance level that not all population proportions are equal to 0.20?
The quality department at an electronics component manufacturer must ensure that their components will operate at prespecified levels. The accompanying table shows a frequency distribution with
Fabco, a precision machining shop, uses statistical process control (SPC) techniques to ensure quality and consistency of their steel shafts. The control limits used in their SPC charts are based on
Total 2005 CEO compensation for the largest U.S. companies by revenue is reported in the following frequency distribution, along with some summary statistics. Total compensation includes salary,
The following frequency distribution shows the distribution of monthly returns for Starbucks Corp. for the years 2003 through 2007.Class (in percent) ...................... FrequencyLess than -5
The data that accompanies this exercise show weekly stock prices for Home Depot.a. Using the Jarque-Bera test, state the competing hypotheses in order to determine whether or not Home Depot's weekly
The data that accompanies this exercise show miles per gallon (MPG) for a sample of 25 cars.a. Using the Jarque-Bera test, state the competing hypotheses in order to determine whether or not MPG
The following frequency distribution shows the monthly stock returns for Home Depot for the years 2003 through 2007.Class (in percent) .................... Observed FrequencyLess than -5
The data that accompany this exercise show various variables, including price and square footage, for 36 single family homes in Arlington, Massachusetts, sold in the first quarter of 2009.a. Use the
An automotive parts company has been besieged with poor publicity over the past few years due to several highly publicized product recalls which have tarnished its public image. This has prompted a
Color coding is often used in manufacturing operations to display production status or to identify/prioritize materials. For example, suppose "green" status indicates that an assembly line is
The operations manager at Electro Tech, an electronics manufacturing company, believes that workers on particular shifts may be more likely to phone in "sick" than those on other shifts. To test this
The human resources department would like to consolidate the current set of retirement plan options offered to specific employee pay groups into a single plan for all pay groups (salaried, hourly, or
A software company develops and markets a popular business simulation/modeling program. A random number generator contained in the program provides random values from various probability
Reorder point decisions for a particular part at an automotive parts distributor are based on the assumption that weekly demand is normally distributed. ("Reorder point" is the inventory level at
Matthew Jordon is a research analyst for a large investment firm. He is preparing a report on the stock performance of Nike, Inc. One aspect of his report will contain inferences concerning monthly
Wenton Power sports produces dune buggies. They have three assembly lines, "Razor," "Blazer," and "Tracer," named after the particular dune buggy models produced on those lines. Each assembly line
In the carbonated beverage industry, dispensing pressure can be an important factor in achieving accurate fill volumes. Too little pressure can slow down the dispensing process. Too much pressure can
The following statistics are computed by sampling from three normal populations whose variances are equal:x1 = 25.3, n1 = 8; x2 = 31.5, n2 = 10; x3 = 32.3, n3 = 6;MSE = 27.2a. Calculate 95%
The following statistics are calculated by sampling from four normal populations whose variances are equal:x1 = 149, n1 = 10; x2 = 154, n2 = 10; x3 = 143, n3 = 10;x4 = 139, n4 = 10; MSE = 51.3a. Use
A one-way analysis of variance experiment produced the following ANOVA table.a. Conduct an ANOVA test at the 5% significance level to determine if some population means differ.b. Calculate 95%
The following Excel output summarizes the results for a one-way analysis of variance experiment in which the treatments were three different hybrid cars and the variable measured was the miles per
In an attempt to improve efficiency, Starbucks has implemented "lean" Japanese techniques at many of its 11,000 U.S. stores (The Wall Street Journal, August 4, 2009). By reducing the time baristas
Elastotech, a plastics company, is trying to determine whether four successive daily batches of their Lexan polycarbonate have the same mean hardness value. Four daily samples of polycarbonate were
Producers of a new grass seed called Pearl's Premium claim that grass grown using its seed blend requires less maintenance as compared to other brands (The Boston Globe, July 4, 2009). For instance,
A production manager is examining whether work shift is related to employee absenteeism. The number of days absent over the past year was tallied for random samples of 25 workers on each shift. A
The following observations were obtained when conducting a two-way ANOVA experiment with no interaction.a. Calculate SST, SSA, SSB, and SSE.b. Calculate MSA, MSB, and MSE.c. Construct an ANOVA
The following observations were obtained when conducting a two-way ANOVA experiment with no interaction.a. Calculate SST, SSA, SSB, and SSE.b. Calculate MSA, MSB, and MSE.c. Construct an ANOVA
A two-way analysis of variance experiment with no interaction is conducted. Factor A has four levels (columns) and Factor B has three levels (rows). The results include the following sum of squares
A two-way analysis of variance experiment with no interaction is conducted. Factor A has three levels (columns) and Factor B has five levels (rows). The results include the following sum of squares
The following table summarizes a portion of the results for a two-way analysis of variance experiment with no interaction.a. Find the missing values in the ANOVA table. b. At the 5% significance
The following table summarizes a portion of the results for a two-way analysis of variance experiment with no interaction.a. Find the missing values in the ANOVA table. b. At the 5% significance
During a typical Professional Golf Association (PGA) tournament, the competing golfers play four rounds of golf, where the hole locations are changed for each round. Here are the scores for the top
The following output summarizes a portion of the results for a two-way analysis of variance experiment with no interaction. Factor A consists of four different kinds of organic fertilizers, factor B
Metalworks, a supplier of fabricated industrial parts, wants to determine if the average output rate for a particular component is the same across the three work shifts. However, since any of four
Given a recent outbreak of illness caused by E. coli bacteria, the mayor in a large city is concerned that some of his restaurant inspectors are not consistent with their evaluations of a
The marketing manager at YumYum, a large deli chain, is testing the effectiveness of four potential advertising strategies. After a two-week trial period for each advertising strategy, sales were
First National Bank employs three real estate appraisers whose job is to establish a property's market value before the bank offers a mortgage to a prospective buyer. It is imperative that each
A two-way analysis of variance experiment with interaction was conducted. Factor A had four levels (columns), factor B had three levels (rows), and five observations were obtained for each
A two-way analysis of variance experiment with interaction was conducted. Factor A had three levels (columns), factor B had five levels (rows), and six observations were obtained for each
A researcher conducts a two-way ANOVA test with interaction and provides the following ANOVA table.a. At the 1% significance level, can you conclude that there is interaction between the two
A researcher conducts a two-way ANOVA test with interaction and provides the following ANOVA table.a. Find the missing values in the ANOVA table.b. At the 5% significance level, can you conclude that
The engineering department at a steel mill is studying the tensile strength of a particular grade of steel when fabricated at various pressures (Factor A) and temperatures (Factor B). The
The effects of detergent brand name (factor A) and the temperature of the water (factor B) on the brightness of washed fabrics are being studied. Four brand names and two temperature levels are used,
The marketing group at Buy4Less, a local retail chain, is examining the effect of advertising at various times of day and on various local television channels. Based on 12-week cycles (4 time periods
A consumer advocate examines whether the longevity of car batteries (measured in years) is affected by the brand name (factor A) and whether or not the car is kept in a garage (factor B). Interaction
A human resource specialist wants to determine whether the average job satisfaction score (on a scale of 0 to 100) is the same for three different industries and three types of work experience. A
It is generally believed that a practical major such as business or engineering can really pay off for college graduates (CNNMoney.com, July 22, 2010). Other studies have shown that it is not just
The Marketing Manager at Foodco, a large grocery store, wants to determine if store display location influences sales of a particular grocery item. He instructs employees to rotate the display
Compressive strength of concrete is affected by several factors, including composition (sand, cement, etc.), mixer type (batch vs. continuous), and curing procedure. Accordingly, a concrete company
The marketing department for an upscale retail catalog company wants to determine if there are differences in the mean customer purchase amounts across the available purchase sources (Internet,
The accompanying table shows a portion of job satisfaction scores (on a scale of 0 to 100) categorized by a person's field of expertise.Field 1Field 2Field
Electrobat, a battery manufacturer, is investigating how storage temperature affects the performance of one of its popular deep-cell battery models used in recreational vehicles. Samples of 30 fully
The accompanying table shows a portion of the results from conducting a two-way ANOVA test with no interaction in which five different production methods (factor A, columns) were evaluated in terms
The following Excel output for Î± = 0.05 summarizes a portion of the results for a two-way ANOVA test without interaction where factor A (column) represents three income categories (low,
An automotive parts manufacturer is testing three potential halogen headlight designs, one of which ultimately will be promoted as providing best-in-class nighttime vision. The distance at which a
At a gymnastics meet, three judges evaluate the balance beam performances of five gymnasts. The judges use a scale of 1 to 10, where 10 is a perfect score.A statistician wants to examine the

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