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applied statistics and multivariate
Questions and Answers of
Applied Statistics And Multivariate
Consider the hemoglobin data in Exercise 8-86.Find the following: (a) An interval that contains 95% of the hemoglobin values with 90% confidence. (b) An interval that contains 99% of the hemoglobin
An operating system for a personal computer has been studied extensively, and it is known that the standard deviation of the response time following a particular command is = 8 milliseconds. A new
The article "Mix Design for Optimal Strength Development of Fly Ash Concrete" (Cement and Concrete Research, 1989, Vol. 19, No. 4, pp. 634-640) investigates the compressive strength of concrete when
An article in the Journal of Sports Science (1987, Vol. 5.pp. 261-271) presents the results of an investigation of the hemoglobin level of Canadian Olympic ice hockey players. The data reported are
A normal population has known mean = 50 and variance o = 5.What is the approximate probability that the sample variance is greater than or equal to 7.44? less than or equal to 2.56? For a random
A normal population has a known mean of 50 and unknown variance. (a) A random sample of n = 16 is selected from this popula tion, and the sample results are 52 and s = 8.How unusual are these
Consider the confidence interval for with known standard deviation : wherea, a,a. Let a 0.05 and find the interval for aaa/2=0.025. Now find the interval for the case a=0.01 and 0.04.Which interval
Consider the bottle-wall thickness measurements described in Exercise 8-40.(a) Compute a 90% tolerance interval on bottle-wall thick- ness that has confidence level 90%. (b) Compute a 90% lower
Consider the fuel rod enrichment data described in Exercise 8-41.Compute a 99% tolerance interval on rod enrichment that has confidence level 95%. Compare the length of the tolerance interval with
Consider the strength-of-concrete data in Exercise 8-37.Compute a 90% tolerance interval on the compressive strength of the concrete that has 90% confidence.
Consider the television tube brightness data in Exercise 8-35.Compute a 99% tolerance interval on the brightness of the television tubes that has confidence level 95%. Compare the length of the
Consider the suspension rod diameter data in Exercise 8-38.Compute a 95% tolerance interval on the diameter of the rods described that has 90% confidence. Compare the length of the tolerance
Consider the rainfall data in Exercise 8-33.Compute a 95% tolerance interval that has confidence level 95%. Compare the length of the tolerance interval with the length of the 95% CI on the
Consider the margarine test described in Exercise 8-36.Compute a 99% tolerance interval on the polyunsaturated fatty acid in this particular type of margarine that has confi- dence level 95%. Compare
Consider the syrup-volume data in Exercise 8-29.Compute a 95% tolerance interval on the syrup volume that has confidence level 90% Compare the length of the tolerance interval with the length of
Consider the Izod impact test described in Exercise 8-28.Compute a 99% tolerance interval on the impact strength of PVC pipe that has confidence level 90%. Compare the length of the tolerance
Consider the tire-testing data in Exercise 8-27.Compute a 95% tolerance interval on the life of the tires that has confidence level 95%. Compare the length of the toler- ance interval with the
How would you obtain a one-sided prediction bound on a future observation? Apply this procedure to obtain a 95% one-sided prediction bound on the wall thickness of the next bottle for the situation
Consider the fuel rod enrichment data described in Exercise 8-41.Compute a 90% prediction interval on the enrichment of the next rod tested. Compare the length of the prediction interval with the
Consider the bottle-wall thickness measurements described in Exercise 8-40.Compute a 90% prediction interval on the wall thickness of the next bottle tested.
Consider the test on the compressive strength of con crete described in Exercise 8-37.Compute a 90% prediction interval on the next specimen of concrete tested.
Consider the suspension rod diameter measurements described in Exercise 8-38.Compute a 95% prediction inter- val on the diameter of the next rod tested. Compare the length of the prediction
Consider the television tube brightness test described in Exercise 8-35.Compute a 99% prediction interval on the brightness of the next tube tested. Compare the length of the prediction interval with
Consider the margarine test described in Exercise 8-36.Compute a 99% prediction interval on the polyunsaturated fatty acid in the next package of margarine that is tested. Compare the length of the
Consider the rainfall in Exercise 8-33.Compute a 95% prediction interval on the rainfall for the next year. Compare the length of the prediction interval with the length of the 95% CI on the
Consider the natural frequency of beams described in Exercise 8-32.Compute a 90% prediction interval on the diameter of the natural frequency of the next beam of this type that will be tested.
Consider the syrup-dispensing measurements de- scribed in Exercise 8-29.Compute a 95% prediction interval on the syrup volume in the next beverage dispensed. Compare the length of the prediction
Consider the Izod impact test described in Exercise 8-28.Compute a 99% prediction interval on the impact strength of the next specimen of PVC pipe tested. Compare the length of the prediction
Consider the tire-testing data described in Exercise 8-27.Compute a 95% prediction interval on the life of the next tire of this type tested under conditions that are similar to those employed in the
An article in the Journal of the American Statistical Association (1990, Vol. 85, pp. 972-985) measured the weight of 30 rats under experiment controls. Suppose that there are 12 underweight rats.
Of 1000 randomly selected cases of lung cancer, 823 resulted in death within 10 years. (a) Calculate a 95% two-sided confidence interval on the death rate from lung cancer. (b) Using the point
The 2004 presidential election exit polls from the crit- ical state of Ohio provided the following results. There were 2020 respondents in the exit polls and 768 were college grad- uates. Of the
The fraction of defective integrated circuits produced in a photolithography process is being studied. A random sam- ple of 300 circuits is tested, revealing 13 defectives. (a) Calculate a 95%
An article in the Australian Journal of Agricultural Research ["Non-Starch Polysaccharides and Broiler Performance on Diets Containing Soyabean Meal as the Sole Protein Concentrate" (1993, Vol. 44,
An article in Cancer Research ["Analyses of Litter- Matched Time-to-Response Data, with Modifications for Recovery of Interlitter Information" (1977, Vol. 37, pp. 3863-3868)] tested the tumorigenesis
An article in Urban Ecosystems. "Urbanization and Warming of Phoenix (Arizona, USA): Impacts, Feedbacks and Mitigation" (2002, Vol. 6, pp. 183-203), mentions that Phoenix is ideal to study the
The percentage of titanium in an alloy used in aero- space castings is measured in 51 randomly selected parts. The sample standard deviation is s = 0.37.Construct a 95% two- sided confidence interval
The sugar content of the syrup in canned peaches is normally distributed. A random sample of n = 10 cans yields a sample standard deviation of s = 4.8 milligrams. Calculate a 95% two-sided confidence
Consider the situation in Exercise 8-44.Find a 99% lower confidence bound on the standard deviation.
A rivet is to be inserted into a hole. A random sample of 15 parts is selected, and the hole diameter is measured. The sample standard deviation of the hole diameter measure- ments is s = 0.008
Determine the x2 percentile that is required to construct each of the following Cls: (a) Confidence level one-sided (upper) 95%, degrees of freedom = 24, (b) Confidence level = 99%, degrees of
An article in Nuclear Engineering International (February 1988, p. 33) describes several characteristics of fuel rods used in a reactor owned by an electric utility in Norway. Measurements on the
The wall thickness of 25 glass 2-liter bottles was mea- sured by a quality-control engineer. The sample mean was = 4.05 millimeters, and the sample standard deviation was s-0.08 millimeter. Find a
An article in Computers & Electrical Engineering ["Parallel Simulation of Cellular Neural Networks" (1996, Vol. 22, pp. 61-84)] considered the speed-up of cellular neural networks (CNN) for a
A machine produces metal rods used in an automobile suspension system. A random sample of 15 rods is selected and the diameter is measured. The resulting data (in millime ters) are as follows: 8.24
The compressive strength of concrete is being tested by a civil engineer. He tests 12 specimens and obtains the following data. 2216 2237 2249 2204 2225 2301 2281 2263 2318 2255 2275 2295 (a) Check
A particular brand of diet margarine was analyzed to determine the level of polyunsaturated fatty acid (in percent- ages). A sample of six packages resulted in the following data: 16.8, 17.2, 17.4,
The brightness of a television picture tube can be eval- uated by measuring the amount of current required to achieve a particular brightness level. A sample of 10 tubes results in -317.2 and
The solar energy consumed (in trillion BTU) in the US. by year from 1989 to 2004 (source: US. Department of Energy Web site, http://www.eia.doc.gov/emeu) is shown in the table below. Read down, then
The Bureau of Meteorology of the Australian Government provided the mean annual rainfall (in milli- meters) in Australia 1983-2002 as follows (http://www.bom.go au climate change/rain03.txt): 499.2,
An article in the Journal of Composite Materials (December 1989, Vol. 23, p. 1200) describes the effect of delam- ination on the natural frequency of beams made from composite laminates. Five such
An article in Obesity Research Impaired Pressure Natriuresis in Obese Youths" (2003, Vol. 11, pp. 745-751)] de- scribed a study in which all meals were provided for 14 lean boys for three days
A postmix beverage machine is adjusted to release a certain amount of syrup into a chamber where it is mixed with carbonated water. A random sample of 25 beverages was found to have a mean syrup
An Izod impact test was performed on 20 specimens of PVC pipe. The sample mean is 7 = 1.25 and the sample stan dard deviation is s = 0.25.Find a 99% lower confidence bound on Izod impact strength.
A random sample has been taken from a normal dis- tribution. Output from a software package is given below: Variable N Mein SE Mean SDev x 1.58 (a) Fill in the missing quantities. Variance Sum 6.11
A random sample has been taken from a normal dis- tribution. Output from a software package is given below: Variable N Mean SE Mean SDev Variance Sum 10 ? 0.507 1.605 7 251.848 (a) Fill in the
Determine the f-percentile that is required to construct each of the following one-sided confidence intervals: (a) Confidence level = 95%, degrees of freedom = 14 (b) Confidence level = 99%, degrees
Determine the e-pereemile that is required to construct each of the following two-sided confidence intervals: (a) Confidence level = 95%, degrees of freedom = 12 (b) Confidence level = 95%, degrees
Find the values of the following percentiles: 15+ 532, and f.
An article in the Journal of Agricultural Science "The Use of Residual Maximum Likelihood to Model Grain Quality Characteristics of Wheat with Variety, Climatic and Nitrogen Fertilizer Effects"
If the sample size is doubled, by how much is the length of the Cl on a in Equation 8-5 reduced? What happens to the length of the interval if the sample size is increased by a factor of four?
By how much must the sample size n be increased if the length of the Cl on a in Equation 8-5 is to be halved?
Suppose that in Exercise 8-14 we wanted the error in estimating the mean life from the two-sided confidence inter- val to be five hours at 95% confidence. What sample size should be used! 817.Suppose
A civil engineer is analyzing the compressive strength of concrete. Compressive strength is normally distributed with = 1000(psi). A random sample of 12 specimens has a mean compressive strength of 7
The life in hours of a 75-watt light bulb is known to be normally distributed with a = 25 hours. A random sample of 20 bulbs has a mean life of T = 1014 hours. (a) Construct a 95% two-sided
A manufacturer produces piston rings for an auto- mobile engine. It is known that ring diameter is normally dis- tributed with a = 0.001 millimeters. A random sample of 15 rings has a mean diameter
The diameter of holes for a cable harness is known to have a normal distribution with r = 0.01 inch. A random sample of size 10 yields an average diameter of 1.5045 inch. Find a 99% two-sided
The yield of a chemical process is being studied. From previous experience, yield is known to be normally distributed and or 3.The past five days of plant operation have resulted in the following
Past experience has indicated that the breaking strength of yarn used in manufacturing drapery material is normally distributed and that = 2 psi. A random sample of nine specimens is tested, and the
Suppose that a = 100 random samples of water from a freshwater lake were taken and the calcium concentration (milligrams per liner) measured. A 95% CI on the mean cal- cium concentration is 0.49 p =
Following are two confidence interval estimates of the mean of the cycles to failure of an automotive door latch mechanism (the test was conducted at an elevated stress level to accelerate the
Consider the gain estimation problem in Exercise 8-4.(a) How large must be if the length of the 95% CI is to be 40? (b) How large must be if the length of the 99% Cl is to be 40?
A random sample has been taken from a normal distri- bution and the following confidence intervals constructed us- ing the same data: (37.53, 49.87) and (35.59, 51.81) (a) What is the value of the
A random sample has been taken from a normal distri- bution and the following confidence intervals constructed us. ing the same data (38.02, 61.98) and (39.95, 60.05) (a) What is the value of the
A confidence interval estimate is desired for the gain in a circuit on a semiconductor device. Assume that gain is not- mally distributed with standard deviation or = 20.(a) Find a 95% CI for a when
Consider the in Equation 8-5 gives 98% confidence? in Equation 8-5 gives 80% confidence! in Equation 8-5 gives 75% confidence! one-sided confidence interval expressions for a mean of a normal
For a normal population with known variance a: (a) What value of (b) What value of (c) What value of
For a normal population with known variance o. answer the following questions: (a) What is the confidence level for the interval - 2.140/V +2140/Vi (b) What is the confidence level for the interval -
Explain the three types of interval estimates: confidence intervals, prediction intervals, and tolerance intervals
Construct a tolerance interval for a normal population
Construct prediction intervals for a future observation
Use a general method for constructing an approximate confidence interval on a parameter
Construct confidence intervals on a population proportion
Construct confidence intervals on the variance and standard deviation of a normal distribution
Construct confidence intervals on the mean of a normal distribution, using either the normal distribution or the t distribution method
for the distribution of the minimum of a sample from an exponential distribution with parameter A.] (b) It can be shown that (T/r) = 1/(r). How does this compare to ) in the uncensored experiment?
Censored Data. A common problem in indus try is life testing of components and systems. In this problem, we will assume that lifetime has an exponen- tial distribution with parameter A, so j = 1/4 =
When the population has a normal distribution, the estimator median (X,- Fl. IX-XI. ---IX-Xl)/0.6745 is sometimes used to estimate the population standard deviation. This estimator is more robust to
Let X be a random variable with mean ja and variance o, and let X, XX, be a random sample of size n from X. Show that the statistic = (XX) is an unbiased estimator for or for an ap propriate choice
Consistent Estimator. Another way to measure the closeness of an estimator to the parameter 0 is in terms of consistency. If O, is an estimator of 9 based on a random sample of observations, O, is
A collection of a randomly selected parts is measured twice by an operator using a gauge. Let X and Y, denote the measured values for the ith part. Assume that these two random variables are
When the sample standard deviation is based on a random sample of size n from a normal population, it can be shown that S is a biased estimator for dr. Specifically, E(S)=2/(-1) (a/2)/[(n - 1)/2] (a)
A lot consists of N transistors, and of these. M (MN) are defective. We randomly select two transis- tors without replacement from this lot and determine whether they are defective or nondefective.
An electric utility has placed special meters on 10 houses in a subdivision that measures the energy consumed (demand) at each hour of the day. They are interested in the en- ergy demand at one
You plan to use a rod to lay out a square, each side of which is the length of the rod. The length of the rod is , which is unknown. You are interested in estimating the area of the square, which is
A random variable x has probability density function f(x)= 28
Let X be a random variable with mean and variancea. Given two independent random samples of sizes w, and w with sample means, and, show that +(-a) < < is an unbiased estimator for. If and are
A manufacturer of semiconductor devices takes a random sample of 100 chips and tests them, classifying each chip as defective or nondefective. Let Xi 0 if the chip is nondefective and Xi 1 if the
A random sample of 36 observations has been drawn from a normal distribution with mean 50 and standard deviation 12.Find the probability that the sample mean is in the interval. Is the assumption of
A procurement specialist has purchased 25 resistors from vendor 1 and 30 resistors from vendor 2.Let X1,1, X1,2, , X1,25 represent the vendor 1 observed resistances, which are assumed to be normally
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