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Questions and Answers of
Statistics
The article "Flexure of Concrete Beams Reinforced with Advanced Composite Orthogrids" (J. of Aerospace Engr., 1997: 7-15) gave the accompanying data on ultimate load (kN) for two different types of
Refer to Exercise 33 in Section 7.3. The cited article also gave the following observations on degree of polymerization for specimens having viscosity times concentration in a higher range:Exercise
The degenerative disease osteoarthritis most frequently affects weight-bearing joints such as the knee. The article "Evidence of Mechanical Load Redistribution at the Knee Joint in the Elderly When
The article "The Effects of a Low-Fat, Plant-Based Dietary Intervention on Body Weight, Metabolism, and Insulin Sensitivity in Postmenopausal Women" (Amer. J. of Med., 2005: 991-997) reported on the
Consider the pooled t variablewhich has a t distribution with m = n - 2 df when both population distributions are normal with Ï1 = Ï2 (see the Pooled t Procedures subsection for
Refer to Exercise 34. Describe the pooled t test for testing H0: µ1 - µ2 = Î0 when both population distributions are normal with Ï1 = Ï2. Then use this
Consider the accompanying data on breaking load (kg/25 mm width) for various fabrics in both an unabraded con dition and an abraded condition ("The Effect of Wet Abrasive Wear on the Tensile
Hexavalent chromium has been identified as an inhalation carcinogen and an air toxin of concern in a number of different locales. The article "Airborne Hexavalent Chromium in Southwestern Ontario"
Adding computerized medical images to a database promises to provide great resources for physicians.However, there are other methods of obtaining such information, so the issue of efficiency of
Scientists and engineers frequently wish to compare two different techniques for measuring or determining the value of a variable. In such situations, interest centers on testing whether the mean
Reliance on solid biomass fuel for cooking and heating exposes many children from developing countries to high levels of indoor air pollution. The article "Domestic Fuels, Indoor Air Pollution, and
Lactation promotes a temporary loss of bone mass to provide adequate amounts of calcium for milk production. The paper "Bone Mass Is Recovered from Lactation to Postweaning in Adolescent Mothers with
Antipsychotic drugs are widely prescribed for conditions such as schizophrenia and bipolar disease. The article "Cardiometabolic Risk of Second- Generation Antipsychotic Medications During First-Time
Many freeways have service (or logo) signs that give information on attractions, camping, lodging, food, and gas services prior to off-ramps. These signs typically do not provide information on
Cushing's disease is characterized by muscular weakness due to adrenal or pituitary dysfunction. To provide effective treatment, it is important to detect childhood Cushing's disease as early as
Refer back to the previous exercise.a. By far the most frequently tested null hypothesis when data is paired is H0: µD = 0. Is that a sensible hypothe sis in this context? Explain.b. Carry out a
Torsion during hip external rotation (ER) and extension may be responsible for certain kinds of injuries in golfers and other athletes. The article "Hip Rotational Velocities During the Full Golf
Example 7.11 gave data on the modulus of elasticity obtained 1 minute after loading in a certain configuration. The cited article also gave the values of modulus of elasticity obtained 4 weeks after
The article "Slender High-Strength RC Columns Under Eccentric Compression" (Magazine of Concrete Res., 2005: 361-370) gave the accompanying data on cylinder strength (MPa) for various types of
Construct a paired data set for which t = ∞ so that the data is highly significant when the correct analysis is used, yet t for the two-sample t test is quite near zero, so the incorrect analysis
Consider the following two questions designed to assess quantitative literacy:What is 15% of 1000? A store is offering a 15% off sale on all TVs. The most popular television is normally priced at
Persons having Reynaud's syndrome are apt to suffer a sudden impairment of blood circulation in fingers and toes. In an experiment to study the extent of this impairment, each subject immersed a
Recent incidents of food contamination have caused great concern among consumers. The article "How Safe Is That Chicken?" (Consumer Reports, Jan. 2010: 19-23) reported that 35 of 80 randomly selected
It is well known that a placebo, a fake medication or treatment, can sometimes have a positive effect just because patients often expect the medication or treatment to be helpful. The article "Beware
Do teachers find their work rewarding and satisfying? The article "Work-Related Attitudes" (Psychological Reports, 1991: 443-450) reports the results of a survey of 395 elementary school teachers and
Olestra is a fat substitute approved by the FDA for use in snack foods. Because there have been anecdotal reports of gastrointestinal problems associated with olestra consumption, a randomized,
Teen Court is a juvenile diversion program designed to circumvent the formal processing of first-time juvenile offenders within the juvenile justice system. The article "An Experimental Evaluation of
a. Use these facts to obtain a large-sample 95% CI formula for estimating ln(θ), and then a CI for θ itself.b. Return to the heart-attack data of Example 1.3, and calculate an interval of
Sometimes experiments involving success or failure responses are run in a paired or before/after manner. Suppose that before a major policy speech by a political candidate, n individuals are selected
Two different types of alloy, A and B, have been used to manufacture experimental specimens of a small tension link to be used in a certain engineering application. The ultimate strength (ksi) of
Using the traditional formula, a 95% CI for p1 - p2 is to be constructed based on equal sample sizes from the two populations. For what value of n (= m) will the resulting interval have a width at
Obtain or compute the following quantities: a. F.05,5,8 b. F.05,8,5 c. F.95,5,8 d. F.95,8,5 e. The 99th percentile of the F distribution with v1 = 10, v2 = 12 f. The 1st percentile of the F
An experiment to compare the tension bond strength of polymer latex modified mortar (Portland cement mortar to which polymer latex emulsions have been added during mixing) to that of unmodified
Give as much information as you can about the P-value of the F test in each of the following situations: a. v1 = 5, v2 = 10, upper-tailed test, f = 4.75 b. v1 = 5, v2 = 10, upper-tailed test, f =
Return to the data on maximum lean angle given in Exercise 28 of this chapter. Carry out a test at significance level .10 to see whether the population standard deviations for the two age groups are
Refer to Example 9.7. Does the data suggest that the standard deviation of the strength distribution for fused specimens is smaller than that for not-fused specimens? Carry out a test at significance
Toxaphene is an insecticide that has been identified as a pollutant in the Great Lakes ecosystem. To investigate the effect of toxaphene exposure on animals, groups of rats were given toxaphene in
The following observations are on time (h) for a AA 1.5- volt alkaline battery to reach a 0.8 voltage ("Comparing the Lifetimes of Two Brands of Batteries," J. of Statistical Educ., 2013,
The article "Enhancement of Compressive Properties of Failed Concrete Cylinders with Polymer Impregnation" (J. of Testing and Evaluation, 1977: 333-337) reports the following data on impregnated
Reconsider the data of Example 9.6, and calculate a 95% upper confidence bound for the ratio of the standard deviation of the triacetate porosity distribution to that of the cotton porosity
The accompanying summary data on compression strength (lb) for 12 Ã 10 Ã 8 in. boxes appeared in the article "Compression of Single-Wall Corrugated Shipping Containers Using
The article "Supervised Exercise Versus Non- Supervised Exercise for Reducing Weight in Obese Adults" (The J. of Sports Med. and Physical Fitness, 2009: 85-90) reported on an investigation in which
Is the response rate for questionnaires affected by including some sort of incentive to respond along with the questionnaire? In one experiment, 110 questionnaires with no incentive resulted in 75
Is there any systematic tendency for part-time college faculty to hold their students to different standards than do full-time faculty? The article "Are There Instructional Differences Between
Shoveling is not exactly a high-tech activity, but it will continue to be a required task even in our information age. The article "A Shovel with a Perforated Blade Reduces Energy Expenditure
The article "Quantitative MRI and Electrophysiology of Preoperative Carpal Tunnel Syndrome in a Female Population" (Ergonomics, 1997: 642-649) reported that (2473.13, 1691.9) was a large-sample 95%
The following summary data on bending strength (lb-in/in) of joints is taken from the article "Bending Strength of Corner Joints Constructed with Injection Molded Splines" (Forest Products J., April,
The article "Urban Battery Litter" cited in Example 8.14 gave the following summary data on zinc mass (g) for two different brands of size D batteries:Assuming that both zinc mass distributions are
The derailment of a freight train due to the catastrophic failure of a traction motor armature bearing provided the impetus for a study reported in the article "Locomotive Traction Motor Armature
Headability is the ability of a cylindrical piece of material to be shaped into the head of a bolt, screw, or other cold-formed part without cracking. The article "New Methods for Assessing Cold
The article "Fatigue Testing of Condoms" cited in Exercise 7.32 reported that for a sample of 20 natural latex condoms of a certain type, the sample mean and sample standard deviation of the number
Information about hand posture and forces generated by the fingers during manipulation of various daily objects is needed for designing high-tech hand prosthetic devices. The article "Grip Posture
The article "Pine Needles as Sensors of Atmospheric Pollution" (Environ. Monitoring, 1982: 273-286) reported on the use of neutron-activity analysis to determine pollutant concentration in pine
The article "The Accuracy of Stated Energy Contents of Reduced-Energy, Commercially Prepared Foods" (J. of the Amer. Dietetic Assoc., 2010: 116-123) presented the accompanying data on vendor-stated
Tensile-strength tests were carried out on two different grades of wire rod ("Fluidized Bed Patenting of Wire Rods," Wire J., June 1977: 56-61), resulting in the accompanying data.a. Does the data
Arsenic is a known carcinogen and poison. The standard laboratory procedures for measuring arsenic concentration (mg/L) in water are expensive. Consider the accompanying summary data and Minitab
The accompanying data on response time appeared in the article "The Extinguishment of Fires Using Low-Flow Water Hose Streams-Part II" (Fire Technology, 1991: 291-320).The authors analyzed the data
Acrylic bone cement is commonly used in total joint arthroplasty as a grout that allows for the smooth transfer of loads from a metal prosthesis to bone structure. The paper "Validation of the
In an experiment to compare bearing strengths of pegs inserted in two different types of mounts, a sample of 14 observations on stress limit for red oak mounts resulted in a sample mean and sample
How does energy intake compare to energy expenditure? One aspect of this issue was considered in the article "Measurement of Total Energy Expenditure by the Doubly Labelled Water Method in
An experimenter wishes to obtain a CI for the difference between true average breaking strength for cables manufactured by company I and by company II. Suppose breaking strength is normally
A study was carried out to compare two different methods, injection and nasal spray, for administering flu vaccine to children under the age of 5. All 8000 children in the study were given both an
Wait staff at restaurants have employed various strategies to increase tips. An article in the Sept. 5, 2005, New Yorker reported that "In one study a waitress received 50% more in tips when she
Suppose a level .05 test of H0: µ1 - µ2 = 0 versus Ha: µ1 - µ2> 0 is to be performed, assuming σ1 = σ 2 = 10 and normality of both distributions, using equal sample sizes (m = n). Evaluate the
The article "Evaluation of a Ventilation Strategy to Prevent Barotrauma in Patients at High Risk for Acute Respiratory Distress Syndrome" (New Engl. J. of Med., 1998: 355-358) reported on an
The invasive diatom species Didymosphenia geminate has the potential to inflict substantial ecological and economic damage in rivers. The article "Substrate Characteristics Affect Colonization by the
Researchers sent 5000 resumes in response to job ads that appeared in the Boston Globe and Chicago Tribune. The resumes were identical except that 2500 of them had "white sounding" first names, such
McNemar's test, developed in Exercise 56, can also be used when individuals are paired (matched) to yield n pairs and then one member of each pair is given treatment 1 and the other is given
The article "Evaluating Variability in Filling Operations" (Food Tech., 1984: 51-55) describes two different filling operations used in a ground-beef packing plant. Both filling operations were set
Let X1,..., Xm be a random sample from a Poisson distribution with parameter µ1, and let Y1,..., Yn be a random sample from another Poisson distribution with parameter µ2. We wish to test
Referring to Exercise 94, develop a large-sample confidence interval formula for µ1- µ2. Calculate the interval for the data given there using a confidence level of 95%.Exercise 94Let
In an experiment to compare the tensile strengths of I = 5 different types of copper wire, J = 4 samples of each type were used. The between-samples and within samples estimates of (2 were computed
In single-factor ANOVA with I treatments and J observations per treatment, let µ = (1/I)(µ.a. Express E(X̅..) in terms of µ.b. Determine E (X̅2i).c. Determine E (X̅2̤ ).d.
An experiment to compare the spreading rates of five different brands of yellow interior latex paint available in a particular area used 4 gallons (J = 4) of each paint. The sample average spreading
Repeat exercise 11, An experiment to compare the spreading rates of five different brands of yellow interior latex paint available in a particular area used 4 gallons (J = 4) of each paint. The
Suppose x̅3. = 427.5. Now which true average spreading rates differ significantly from one another? Be sure to use the method of underscoring to illustrate your conclusions, and write a paragraph
Use Tukey's procedure on the data in Example 10.3 to identify differences in true average bond strengths among the five protocols?
Exercise 10.7 described an experiment in which 26 resistivity observations were made on each of six different concrete mixtures. The article cited there gave the following sample means: 14.18, 17.94,
Reconsider the axial stiffness data given in Exercise 8. ANOVA output from Minitab follows:Pooled StDev = 32.39. Tukey's pair-wise comparisons Family error rate = 0.0500 Individual error rate =
Refer to Exercise 5.Consider the following summary data on the modulus of elasticity (Ã 106 psi) for lumber of three different grades [in close agreement with values in the article
Consider the accompanying data on plant growth after the application of five different types of growth hormone.a. Perform an F test at level a = .05. b. What happens when Tukey's procedure is applied?
Consider a single-factor ANOVA experiment in which I = 3, J = 5, x̅1. = 10, x̅2. = 12, and x̅3. = 20. Find a value of SSE for which f . > F.05,2,12, so that H0: µ1 = µ2 = µ3 is rejected, yet
Suppose that the compression-strength observations on the fourth type of box in Example 10.1 had been 655.1, 748.7, 662.4, 679.0, 706.9, nd 640.0 (obtained by dding 120 to each previous x4j).
The article "The Effect of Enzyme Inducing Agents on the Survival Times of Rats Exposed to Lethal Levels of Nitrogen Dioxide" (Toxicology and Applied Pharmacology, 1978: 169-174) reports the
The following data refers to yield of tomatoes (kg/plot) for four different levels of salinity. Salinity level here refers to electrical conductivity (EC), where the chosen levels were EC = 1.6, 3.8,
Apply the modified Tukey's method to the data in Exercise 22 to identify significant differences among the µi's?
The accompanying summary data on skeletal-muscle CS activity (nmol/min/mg) appeared in the article "Impact of Lifelong Sedentary Behavior on Mitochondrial Function of Mice Skeletal Muscle" (J. of
Lipids provide much of the dietary energy in the bodies of infants and young children. There is a growing interest in the quality of the dietary lipid supply during infancy as a major determinant of
Samples of six different brands of diet/imitation margarine were analyzed to determine the level of physiologically active polyunsaturated fatty acids (PAPFUA, in percentages), resulting in the
Although tea is the world's most widely consumed beverage after water, little is known about its nutritional value. Folacin is the only B vitamin present in any significant amount in tea, and recent
For a single-factor ANOVA with sample sizes Ji (i = 1, 2,...I), show that SSTr = (Ji (X̅i. - X̅...)2 = (Ji X̅2i. - X̅2̤ where n = (Ji?
When sample sizes are equal (Ji = J), the parameters a1, a2, ... aI of the alternative parameterization are restricted by (ai = 0. For unequal sample sizes, the most natural restriction is (Ji ai =
The lumen output was determined for each of I = 3 different brands of light-bulbs having the same wattage, with J = 8 bulbs of each brand tested. The sums of squares were computed as SSE = 4773.3 and
Reconsider Example 10.8 involving an investigation of the effects of different heat treatments on the yield point of steel ingots. a. If J = 8 and ( = 1, what is β for a level .0 = F test when µ1 =
When sample sizes are not equal, the non-centrality parameter is (Jia2i / (2 and (2 = (1/I) (Jia2i / (2. Referring to Exercise 22, what is the power of the test when µ2 = µ3, µ1 = µ2 - (, and µ4
In an experiment to compare the quality of four different brands of magnetic recording tape, five 2400-ft reels of each brand (A-D) were selected and the number of flaws in each reel was
Suppose that Xij is a binomial variable with parameters n and pi (so approximately normal when npi $ 10 and nqi ≥ 10. Then since µi = npi, V(Xij) = (2i = npi(1 - pi) = µi(1 - µi / n). How should
Simplify E(MSTr) for the random effects model when J1 = J2 = ... = JI = J?
An experiment was carried out to compare flow rates for four different types of nozzle. a. Sample sizes were 5, 6, 7, and 6, respectively, and calculations gave f = 3.68. State and test the relevant
Cortisol is a hormone that plays an important role in mediating stress. There is growing awareness that exposure of outdoor workers to pollutants may impact cortisol levels. The article "Plasma
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