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applied statistics and multivariate

Questions and Answers of Applied Statistics And Multivariate

Use the sign test on the blood cholesterol data in Exercise 10-41.Is there evidence that diet and exercise reduce the median cholesterol level?
The manager of a fleet of automobiles is testing two brands of radial tires. He assigns one tire of each brand at random to the two rear wheels of eight cars and runs the cars until the tires wear
Consider the shear strength experiment described in Example 10-10.(a) Construct a 95% confidence interval on the difference in mean shear strength for the two methods. Is the result you obtained
Consider the distance traveled by a golf ball in Exercise 10-29.(a) Use the Wilcoxon rank-sum test to investigate if the means differ. Use 0.05.(b) Use the normal approximation for the Wilcoxon
Consider the pipe deflection data in Exercise 10-18.(a) Use the Wilcoxon rank-sum test for the pipe deflection temperature experiment. If 0.05, what are your conclusions?(b) Use the normal
The manufacturer of a hot tub is interested in testing two different heating elements for his product. The element that produces the maximum heat gain after 15 minutes would be preferable. He obtains
An electrical engineer must design a circuit to deliver the maximum amount of current to a display tube to achieve sufficient image brightness. Within her allowable design constraints, she has
The overall distance traveled by a golf ball is tested by hitting the ball with Iron Byron, a mechanical golfer with a swing that is said to emulate the legendary champion, Byron Nelson. Ten randomly
An article in Technometrics (1999, Vol. 41, pp.202–211) studied the capability of a gauge by measuring the weights of two sheets of paper. The data are shown below.Paper Observations 1 3.481 3.448
An article in Radio Engineering and Electronic Physics (1984, Vol. 29, No. 3, pp. 63–66) investigated the behavior of a stochastic generator in the presence of external noise. The number of periods
An article in IEEE International Symposium on Electromagnetic Compatibility (2002, Vol. 2, pp. 667–670)quantified the absorption of electromagnetic energy and the resulting thermal effect from
An article in Electronic Components and Technology Conference (2001, Vol. 52, pp. 1167–1171) compared single versus dual spindle saw processes for copper metallized wafers. A total of 15 devices of
Two companies manufacture a rubber material intended for use in an automotive application. The part will be subjected to abrasive wear in the field application, so we decide to compare the material
The melting points of two alloys used in formulating solder were investigated by melting 21 samples of each material. The sample mean and standard deviation for alloy 1 was and , while for alloy 2
Two suppliers manufacture a plastic gear used in a laser printer. The impact strength of these gears measured in foot-pounds is an important characteristic. A random sample of 10 gears from supplier
In semiconductor manufacturing, wet chemical etching is often used to remove silicon from the backs of wafers prior to metallization. The etch rate is an important characteristic in this process and
The deflection temperature under load for two different types of plastic pipe is being investigated. Two random samples of 15 pipe specimens are tested, and the deflection temperatures observed are
Two catalysts may be used in a batch chemical process. Twelve batches were prepared using catalyst 1, resulting in an average yield of 86 and a sample standard deviation of 3.Fifteen batches were
An article in Fire Technology investigated two different foam expanding agents that can be used in the nozzles of fire-fighting spray equipment. A random sample of five observations with an aqueous
The concentration of active ingredient in a liquid laundry detergent is thought to be affected by the type of catalyst used in the process. The standard deviation of active concentration is known to
A polymer is manufactured in a batch chemical process. Viscosity measurements are normally made on each batch, and long experience with the process has indicated that the variability in the process
Two different formulations of an oxygenated motor fuel are being tested to study their road octane numbers. The variance of road octane number for formulation 1 is 1.5, and for formulation 2 it is
Explain and use the relationship between confidence intervals and hypothesis tests
Compute power, type II error probability, and make sample size decisions for two-sample tests on means, variances, and proportions
Use the P-value approach for making decisions in hypotheses tests
Test hypotheses and construct confidence intervals on the difference in two population proportions
Test hypotheses and construct confidence intervals on the ratio of the variances or standard deviations of two normal distributions
Test hypotheses and construct confidence intervals on the difference in means of two normal distributions
Structure comparative experiments involving two samples as hypothesis tests
Consider the television picture tube brightness experiment described in Exercise 8-35.(a) For the sample size n 10, do the data support the claim that the standard deviation of current is less than
Consider the fatty acid measurements for the diet margarine described in Exercise 8-36.(a) For the sample size n 6, using a two-sided alternative hypothesis and 0.01, test H0:2 1.0.(b)
Consider the dissolved oxygen data in Exercise 8-94.Water quality engineers are interested in knowing whether these data support a claim that mean dissolved oxygen concentration is 2.5 milligrams per
Consider the golf ball overall distance data in Exercise 6-33.(a) Do these data support the claim that the mean overall distance for this brand of ball does not exceed 270 yards?Use 0.05.(b) What
Consider the 20 observations collected on the number of errors in a string of 1000 bits of a communication channel given in Exercise 6-94.(a) Based on the description of the random variable and these
Consider the 40 observations collected on the number of nonconforming coil springs in production batches of size 50 given in Exercise 6-93.(a) Based on the description of the random variable and
A biotechnology company produces a therapeutic drug whose concentration has a standard deviation of 4 grams per liter. A new method of producing this drug has been proposed, although some additional
A manufacturer of precision measuring instruments claims that the standard deviation in the use of the instruments is at most 0.00002 millimeter. An analyst, who is unaware of the claim, uses the
The mean pull-off force of an adhesive used in manufacturing a connector for an automotive engine application should be at least 75 pounds. This adhesive will be used unless there is strong evidence
The marketers of shampoo products know that customers like their product to have a lot of foam. A manufacturer of shampoo claims that the foam height of his product exceeds 200 millimeters. It is
Suppose that in Exercise 9-126, the experimenter had believed that 14.For each of the following sample sizes, and a fixed 0.05, find the probability of a type II error if the true mean is 205
An inspector of flow metering devices used to administer fluid intravenously will perform a hypothesis test to determine whether the mean flow rate is different from the flow rate setting of 200
Consider the situation of Exercise 9-124.After collecting a sample, we are interested in testing H0: p 0.10 versus with 0.05. For each of the following situations, compute the p-value for this
A manufacturer of semiconductor devices takes a random sample of size n of chips and tests them, classifying each chip as defective or nondefective. Let Xi 0 if the chip is nondefective and Xi 1
Suppose we wish to test the hypothesis H0: 85 versus the alternative H1: 85 where 16.Suppose that the true mean is 86 and that in the practical context of the problem this is not a
An article in Fire Technology [“An Experimental Examination of Dead Air Space for Smoke Alarms” (Vol. 45, 2009, pp. 97–115)] studied the performance of smoke detectors installed not less than
The diameter of a ball bearing was measured by an inspector using a new type of caliper. The results were as follows (in mm): 0.265, 0.263, 0.266, 0.267, 0.267, 0.265, 0.267, 0.267, 0.265, 0.268,
Consider the compressive strength data in Exercise 8-37.(a) Use the sign test to investigate the claim that the median strength is at least 2250 psi. Use 0.05.(b) Use the normal approximation to test
Consider the margarine fat content data in Exercise 8-36.Use the sign test to test versus with 0.05.(a) Find the P-value for the test statistic and use this quantity to make your decision.(b) Use the
The impurity level (in ppm) is routinely measured in an intermediate chemical product. The following data were observed in a recent test:2.4, 2.5, 1.7, 1.6, 1.9, 2.6, 1.3, 1.9, 2.0, 2.5, 2.6, 2.3,
The titanium content in an aircraft-grade alloy is an important determinant of strength. A sample of 20 test coupons reveals the following titanium content (in percent):8.32, 8.05, 8.93, 8.65, 8.25,
Ten samples were taken from a plating bath used in an electronics manufacturing process, and the bath pH was determined. The sample pH values are 7.91, 7.85, 6.82, 8.01, 7.46, 6.95, 7.05, 7.35, 7.25,
Reconsider Exercise 6-71.The data were the number of earthquakes per year of magnitude 7.0 and greater since 1900.(a) Use computer software to summarize these data into a frequency distribution.
The number of cars passing eastbound through the intersection of Mill and University Avenues has been tabulated by a group of civil engineering students. They have obtained the data in the adjacent
Define X as the number of underfilled bottles from a filling operation in a carton of 24 bottles. Seventy-five cartons are inspected and the following observations on X are recorded:Values 0 1 2 3
Let X denote the number of flaws observed on a large coil of galvanized steel. Seventy-five coils are in spected and the following data were observed for the values of X:Values 1 2 3 4 5 6 7 8
Exercise 6-33 describes testing golf balls for an overall distance standard.(a) Can you support a claim that mean distance achieved by this particular golf ball exceeds 280 yards? Use 0.05.Find
Exercise 6-30 gave data on the heights of female engineering students at ASU.(a) Can you support a claim that the mean height of female engineering students at ASU is at least 65 inches? Use 0.05.
Reconsider the television tube brightness experiment in Exercise 8-35.Suppose that the design engineer claims that this tube will require at least 300 microamps of current to produce the desired
Reconsider the tire testing experiment described in Exercise 8-27.(a) The engineer would like to demonstrate that the mean life of this new tire is in excess of 60,000 kilometers. Formulate and test
Consider the dissolved oxygen concentration at TVA dams first presented in Exercise 8-94.(a) Test the hypothesis H0: 4 versus . Use 0.01. Find the P-value.(b) Check the normality assumption.(c)
Consider the baseball coefficient of restitution data first presented in Exercise 8-92.(a) Do the data support the claim that the mean coefficient of restitution of baseballs exceeds 0.635? Use
The sodium content of twenty 300-gram boxes of organic cornflakes was determined. The data (in milligrams) are as follows: 131.15, 130.69, 130.91, 129.54, 129.64, 128.77, 130.72, 128.33, 128.24,
Cloud seeding has been studied for many decades as a weather modification procedure (for an interesting study of this subject, see the article in Technometrics, “A Bayesian Analysis of a
A 1992 article in the Journal of the American Medical Association (“A Critical Appraisal of 98.6 Degrees F, the Upper Limit of the Normal Body Temperature, and Other Legacies of Carl Reinhold
An article in the ASCE Journal of Energy Engineering (1999, Vol. 125, pp. 59–75) describes a study of the thermal inertia properties of autoclaved aerated concrete used as a building material. Five
Medical researchers have developed a new artificial heart constructed primarily of titanium and plastic. The heart will last and operate almost indefinitely once it is implanted in the patient’s
A bearing used in an automotive application is supposed to have a nominal inside diameter of 1.5 inches. A random sample of 25 bearings is selected and the average inside diameter of these bearings
A melting point test of n 10 samples of a binder used in manufacturing a rocket propellant resulted in Assume that the melting point is normally distributed with .(a) Test H0: 155 versus H1:
The mean water temperature downstream from a power plant cooling tower discharge pipe should be no more than 100°F. Past experience has indicated that the standard deviation of temperature is 2°F.
A hypothesis will be used to test that a population mean equals 10 against the alternative that the population mean is greater than 10 with known variance . What is the critical value for the test
State the null and alternative hypothesis in each case.(a) A hypothesis test will be used to potentially provide evidence that the population mean is greater than 10.(b) A hypothesis test will be
If we plot the probability of accepting H0:0 versus various values of and connect the points with a smooth curve, we obtain the operating characteristic curve(or the OC curve) of the test procedure.
A random sample of 500 registered voters in Phoenix is asked if they favor the use of oxygenated fuels year-round to reduce air pollution. If more than 400 voters respond positively, we will conclude
The proportion of residents in Phoenix favoring the building of toll roads to complete the freeway system is believed to be p 0.3. If a random sample of 10 residents shows that 1 or fewer favor
The proportion of adults living in Tempe, Arizona, who are college graduates is estimated to be p 0.4. To test this hypothesis, a random sample of 15 Tempe adults is selected. If the number of
In Exercise 9-20, find the boundary of the critical region if the type I error probability is(a) 0.01 and n 8 (c) 0.01 and n 16(b) 0.05 and n 8 (d) 0.05 and n 16
A manufacturer is interested in the output voltage of a power supply used in a PC. Output voltage is assumed to be normally distributed, with standard deviation 0.25 volt, and the manufacturer wishes
In Exercise 9-15, calculate the P-value if the observed statistic is(a) = 180 (b) = 190 (c) = 170
Repeat Exercise 9-15 assuming that the sample size is n 16 and the boundary of the critical region is the same.
A consumer products company is formulating a new shampoo and is interested in foam height (in millimeters).Foam height is approximately normally distributed and has a standard deviation of 20
In Exercise 9-10, calculate the P-value if the observed statistic is(a) = 98 (b) = 101 (c) = 102
In Exercise 9-10, find the boundary of the critical region if the type I error probability is(a) 0.01 and n 9 (c) 0.01 and n 5(b) 0.05 and n 9 (d) 0.05 and n 5
Compute power and type II error probability, and make sample size selection decisions for tests on means, variances, and proportions
Use the P-value approach for making decisions in hypotheses tests
Test hypotheses on a population proportion
Test hypotheses on the variance or standard deviation of a normal distribution
Test hypotheses on the mean of a normal distribution using either a Z-test or a t-test procedure
Structure engineering decision-making problems as hypothesis tests
Suppose that X X X is a random sample from a continuous probability distribution with median. (a) Show that P{min(X) < < max{X}} Hiar: The complement of the event [min(X)
It is possible to construct a nonparametric tol- erance interval that is based on the extreme values in a random sample of size n from any continuous population. If p is the minimum proportion of the
Consider a two-sided confidence interval for the mean when or is known: wherea, a, a.lfa,a, a/2, we have the usual 100(-a)% confidence interval for u. In the above, whena, a, the interval is not
An electrical component has a time-to-failure (or lifetime) distribution that is exponential with param- eter , so the mean lifetime is = 1/A. Suppose that a sample of n of these components is put on
An article in the Journal of Human Nutrition and Dietetics "The Validation of Energy and Protein Intakes by Doubly Labeled Water and 24-Hour Urinary Nitrogen Excretion in Post-Obese Subjects" (1995,
An article in the Journal of Applied Physiology ["Humidity Does Not Affect Central Nervous System Oxygen Toxicity" (2001, Vol. 91, pp. 1327-1333)] reported that central nervous system (CNS) oxygen
An article in Engineering Horizons (Spring 1990, p. 26) reported that 117 of 484 new engineering graduates were planning to continue studying for an advanced degree. Consider this as a random sample
The tar content in 30 samples of cigar tobacco follows: 1.542 1.585 1.532 1.466 1.499 1.611 1.622 1.440 1.608 1.520 1.466 1.546 1.494 1.548 1.626 1.478 1.542 1.511 1.459 1.533 1.532 1.523 1.397 1.487
Consider the baseball coefficient of restitution data in Exercise 8-92.Suppose that any baseball that has a coefficient of restitution that exceeds 0.635 is considered too lively. Based on the
During the 1999 and 2000 baseball seasons, there was much speculation that the unusually large number of home runs that were hit was due at least in part to a livelier ball. One way to test the
The maker of a shampoo knows that customers like this product to have a lot of foam. Ten sample bottles of the product are selected at random and the foam heights observed are as follows (in
Consider the compressive strength of concrete data from Exercise 8-87.Find a 95% prediction interval on the next sample that will be tested.

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