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Questions and Answers of Statistics

For the NHL data in Exercise 12-11(a) Find the equation that minimizes Cp.(b) Find the equation that minimizes MSE.(c) Find the equation that maximizes the adjusted R2. Is this the same equation you
We have used a sample of 30 observations to fit a regression model. The full model has nine regressors, the variance once estimate is 2 = MSE = 100, and R2 = 0.92. (a) Calculate the F-statistic for
A sample of 25 observations is used to fit a regression model in seven variables. The estimate of σ2 for this full model is MSE = 10. (a) A forward selection algorithm has put three of the
The data shown in the table on page 464 represent the thrust of a jet-turbine engine (y) and six candidate regressors: x1 = primary speed of rotation, x2 = secondary speed of rotation, x3 = fuel flow
Consider the engine thrust data in Exercise 12-64.Refit the model using as the response variable and x*3 = ln x3 as the regressor (along with x4 and x5).(a) Test for significance of regression using
The transient points of an electronic inverter are influenced by many factors. Table 12-20 gives data on the transient point (y, in volts) of PMOS-NMOS inverters and five candidate regressors:, x1 =
Consider the inverter data in Exercise 12-66. Delete observation 2 from the original data. Define new variables as follows:And(a) Fit a regression model using these transformed regressors (do not use
Following are data on y = green liquor (g/l) and x = paper machine speed (feet per minute) from a Kraft paper machine. (The data were read from a graph in an article in the Tappi Journal, March
Consider the jet engine thrust data in Exercise 12-64.(a) Use all possible regressions to select the best regression equation, where the model with the minimum value of MSE is to be selected as
Consider the electronic inverter data in Exercise 12-66 and 12-67. Define the response and regressors variables as in Exercise 12-67, and delete the second observation in the sample.(a) Use all
Consider the three-variable regression model for the jet engine thrust data in Exercise 12-65. Calculate the variance inflation factors for this model. Would you conclude that multicollinearity is a
A multiple regression model was used to relate y = viscosity of a chemical product to x1 = temperature and x2 = reaction time. The data set consisted of n = 15 observations.(a) The estimated
An article in the Journal of the American Ceramics Society (Vol. 75, 1992, pp. 112–116) describes a process for immobilizing chemical or nuclear wastes in soil by dissolving the contaminated soil
In Design and Analysis of Experiments, 5th edition (John Wiley & Sons, 2001) D. C. Montgomery describes an experiment in which the tensile strength of a synthetic fiber is of interest to the
In €œOrthogonal Design for Process Optimization and Its Application to Plasma Etching€ (Solid State Technology, May 1987), G. Z. Yin and D. W. Jillie describe an experiment to
The compressive strength of concrete is being studied, and four different mixing techniques are being investigated. The following data have been collected.(a) Test the hypothesis that mixing
An experiment was run to determine whether four specific firing temperatures affect the density of a certain type of brick. The experiment led to the following data.(a) Does the firing temperature
An electronics engineer is interested in the effect on tube conductivity of five different types of coating for cathode ray tubes in a telecommunications system display device. The following
The response time in milliseconds was determined for three different types of circuits in an electronic calculator. The results are recorded here.(a) Using a = 0.01, test the hypothesis that the
An article in the ACI Materials Journal (Vol. 84, 1987, pp. 213€“216) describes several experiments investigating the rodding of concrete to remove entrapped air. A 3-inch x 6-inch cylinder
An article in Environment International (Vol. 18, No. 4, 1992) describes an experiment in which the amount of radon released in showers was investigated. Radon-enriched water was used in the
A paper in the Journal of the Association of Asphalt Paving Technologists (Vol. 59, 1990) describes an experiment to determine the effect of air voids on percentage retained strength of asphalt. For
An article in the Materials Research Bulletin (Vol. 26, No. 11, 1991) investigated four different methods of preparing the superconducting compound PbMo6S8. The authors contend that the presence of
Use Fisher’s LSD method with a = 0.05 to analyze the means of the five different levels of cotton content in Exercise 13-1.
Use Fisher’s LSD method with a = 0.05 test to analyze the means of the three flow rates in Exercise 13-2.
Use Fisher’s LSD method with a = 0.05 to analyze the mean compressive strength of the four mixing techniques in Exercise 13-3.
Use Fisher’s LSD method to analyze the five means for the coating types described in Exercise 13-5. Use a = 0.01.
Use Fisher’s LSD method to analyze the mean response times for the three circuits described in Exercise 13-6. Use a = 0.01.
Use Fisher’s LSD method to analyze the mean amounts of radon released in the experiment described in Exercise 13-8. Use a = 0.05.
Apply Fisher’s LSD method to the air void experiment described in Exercise 13-9. Using a = 0.05, which treatment means are different?
Apply Fisher’s LSD method to the superconducting material experiment described in Exercise 13-10. Which preparation methods differ, if a = 0.05?
Suppose that four normal populations have common variance μ2 = 25 and means μ1 = 50, μ2 = 60, μ3 = 50, and μ4 = 60. How many observations should be taken on each population
Suppose that five normal populations have common variance σ2 = 100 and means μ1 = 175, μ2 = 190, μ3 = 160, μ4 =200, and μ5 = 215. How many observations per population
A textile mill has a large number of looms. Each loom is supposed to provide the same output of cloth per minute. To investigate this assumption, five looms are chosen at random, and their output is
An article in the Journal of the Electrochemical Society (Vol. 139, No. 2, 1992, pp. 524€“532) describes an experiment to investigate the low-pressure vapor deposition of polysilicon. The
An article in the Journal of Quality Technology (Vol. 13, No. 2, 1981, pp. 111€“114) describes an experiment that investigates the effects of four bleaching chemicals on pulp brightness.
Consider the vapor-deposition experiment described in Exercise 13-22.(a) Estimate the total variability in the uniformity response.(b) How much of the total variability in the uniformity response is
In €œThe Effect of Nozzle Design on the Stability and Performance of Turbulent Water Jets€ (Fire Safety Journal, Vol. 4, August 1981), C. Theobald describes an experiment in
In Design and Analysis of Experiments, 5th edition (John Wiley & Sons, 2001), D. C. Montgomery describes an experiment that determined the effect of four different types of tips in a hardness tester
An article in the American Industrial Hygiene Association Journal (Vol. 37, 1976, pp. 418€“422) describes a field test for detecting the presence of arsenic in urine samples.The test has
An article in the Food Technology Journal (Vol. 10, 1956, pp. 39–42) describes a study on the prospecting content of tomatoes during storage. Four storage times were selected, and samples from nine
An experiment was conducted to investigate leaking current in a SOS MOSFETS device. The purpose of the experiment was to investigate how leakage current varies as the channel length changes. Four
Consider the leakage voltage experiment described in Exercise 13-29. The observed leakage voltage for channel length 4 and width 5 was erroneously recorded. The correct observation is 4.0. Analyze
An article in the IEEE Transactions on Components, Hybrids, and Manufacturing Technology (Vol. 15, No. 2, 1992, pp. 146€“153) describes an experiment in which the contact resistance of a
An article in Lubrication Engineering (December 1990) describes the results of an experiment designed to investigate the effects of carbon material properties on the progression of blisters on carbon
Apply the Fisher LSD method to the experiment in Exercise 13-32. Summarize your conclusions regarding the effect of material type on surface roughness.
An article in the Journal of Quality Technology (Vol. 14, No. 2, 1982, pp. 80€“89) describes an experiment in which three different methods of preparing fish are evaluated on the basis of
An article in the Journal of Agricultural Engineering Research (Vol. 52, 1992, pp. 53€“76) describes an experiment to investigate the effect of drying temperature of wheat grain on the
An article in Agricultural Engineering (December 1964, pp. 672€“673) describes an experiment in which the daily weight gain of swine is evaluated at different levels of housing temperature.
An article in Communications of the ACM (Vol. 30, No. 5, 1987) studied different algorithms for estimating software development costs. Six algorithms were applied to eight software development
Consider an ANOVA situation with a = 4 means μ1 = 1, μ2 = 5, μ3 = 8, and μ4 = 4. Suppose that σ2 = 4, n = 4, and a = 0.05. (a) Find the power of the ANOVA F-test. (b) How
Consider an ANOVA situation with a = 5 treatments. Let σ2 = 9 and a = 0.05, and suppose that n = 4. (a) Find the power of the ANOVA F-test when μ1 = μ2 = μ3 = 1, μ4 = 3, and
Apply the maximum likelihood method to the normal distribution with μ = 0.
Extend Prob. 3 as follows, suppose that m time’s n trials were made and in the first n trials A happened k1 times, in the second n trials A happened k2 times, in the mth n trials A happened km
Consider X = Number of independent trials until an event A occurs, show that X has the probability function f(x) = pqx–1, x = 1, 2, ∙∙∙, where p is the probability of A in a
Does the interval in Prob. 1 get longer or shorter it we take y = 0.99 instead of 0.95? by what factor
Find a 90% confidence interval for the mean μ of a normal population with variance 0.25, using a sample of 100 values with mean 212.3.
Use of Fig. 525 find a 95% confidence interval for a sample of 200 values with mean 120 from a normal distribution with variance 4, using Fig. 525.
Find a 99% confidence interval for the mean of a normal population from the sample 425, 420, 425, 435.
Knoop hardness of diamond 9500, 9800, 9750, 9200, 9400, 9550Find a 99 % confidence interval for the mean of a normal population from the sample
Melting point (°C) of aluminum 600, 667, 654, 663, 662Find a 99 % confidence interval for the mean of a normal population from the sample:
Find a 99% confidence interval for p in the binomial distribution from a classical result by K. Pearson, who in 24000 trials of tossing a coin obtained 12012 Heads; do you think that the coin was
If the weight X of bags of cement is normally distributed with a mean of 40kg and a standard deviation of 2kg how may bags can a delivery truck carry so that the probability of the total load
In one of his classical experiments Buffon obtained 2048 heads in tossing a coin 4040 times, was the coin fair?
Assuming normality and known variance σ2 = 4, test the hypothesis μ = 30.0 against the alternative(a) μ = 28.5,(b) μ = 30.7, using a sample of size 10 with mean x̅ = 28.5 and choosing α = 5%.
Determine the power of the test in Prob. 4(a).
Using the sample 0.80, 0.81, 0.81, 0.82, 0.81, 0.82, 0.80, 0.81, 0.81, (length of nails in inches), test the hypothesis μ = 0.80 in. (the length indicated on the box) against the alternative
If a sample of 50 tires of a certain kind has a mean life of 32 000 mi and standard deviation of 4000 mi, can the manufacturer claim that the true mean life of such tires is greater than 30 000mi?
If a standard medication cures about 70% of patients with a certain disease and a new medication cured 148 of the first 200 patients on whom it was tried, can we conclude that the new medication is
Suppose that in operating battery-powered electrical equipment, it is less expensive to replace all batteries at fixed intervals than to replace each battery individually when it breaks down,
The two samples 70, 80, 30, 70, 60, 80 and 140, 120, 130, 120, 120, 130, 120 are values of the differences of temperatures (°C) of iron at two stages of casting, taken from two different crucibles.
Find the binomial approximation of the hypergeometric distribution in Example 1 and compare the approximate and the accurate values.
Calculate P(A; θ) in Example 1 if the sample size is increased from n = 2 to n = 3, the other data remaining as before. Compute P (A; 0.10) and P(A; 0.20) and compare with Example 1.
If in a single sampling plan for large lots of spark plugs, the sample size is 100 and we want the AQL to be 5% and the producer’s risk 2%, what acceptance number c should we choose? (Use the
Graph and compare sampling plans with c = 1 and increasing values of n, say, n = 2, 3, 4. (Use the binomial distribution).
Graph the OC curve and the AOQ curve for the single sampling plan for large lots with n = 5 and c = 0, and find the AOQL.
If in 10 flips of a coin we get the same ratio as in Prob. 1(3 heads and 7 tails), is the conclusion the same as in Prob. 1? First conjecture, then compute
If in rolling a die 180 times we get 39, 22, 41, 26, 20, 32, can we claim on the 5% level that the die is fair?
A manufacturer claims that in a process of producing kitchen knives, only 2.5% of the knives are dull. Test the claim against the alternative that more than 2.5% of the knives are dull, using a
Test for normality at the 1% level using a sample of n = 79 (rounded) values x (tensile strength [kg/mm2] of steel sheets of 0.3 mm thickness). a = a(x) = absolute frequency. (Take the first two
Three samples of 200 rivets each were taken from a large production of each of three machines. The numbers of defective rivets in the samples were 7, 8, and 12. Is this difference significant?
Are the 5 tellers in a certain bank equally time-efficient if during the same time interval on a certain day they serve 120, 95, 110, 108, 102 customers?
Difficulty with Random Selection 77 students were asked to choose 3 of the integers 11, 12, 13, ˆ™ˆ™ˆ™, 30 completely arbitrarily, the amazing result was as follows.If
Does a process of producing plastic pipes of length μ = 2 meters need adjustment if in a sample, 4 pipes have the exact length and 15 are shorter and 3 longer than 2 meters? (Use the normal
Test whether a thermostatic switch is properly set to 20oC against the alternative that its setting is too low, use a sample of 9 values, 8 of which are less than 20oC and 1 is greater than 20oC.
Set up a sign test for the lower quartile q25 (defined by the condtion F (q25) = 0.25).
Apply the test explained in Example 2 to the following data (x = diastolic blood pressure [mm Hg], y = weight of heart [in grams] of 10 pateients who died of cerebrl hemorrhage).
Does the amount of fertilizer increase the yield of wheat X [kg/pl0t]? Use a sample of values ordered according to increasing amounts of fertilizer; 41.4, 43.3, 39.6, 43.0, 44.1, 45.6, 44.5, 46.7.
Determine a 95% confidence interval for the mean μ of a normal population with variance σ2 = 16, using a sample of size 400 with mean 53.
Determine a 99% confidence interval for the mean of a normal population with standard deviation 2.2, using the sample 28, 24, 31, 27, 22.
Assuming normality, find a 95% confidence interval for the variance from the sample 145.3, 145.4, 146.2.
A sample of size n = 128 with variance s2 = 1.921
A firm sells paint in cans containing 1 kg of paint per can and is interested to know whether the mean weight differs significantly from 1kg, in which case the filling machine must be adjusted. Set
In Prob. 33, change the alternative to μ ≠ 15.0 and test as before.
Drawing 4 screws from a lot of right handed and left handed screws.Graph a sample space for the experiments
Tossing a coin until the first Head appears
Drawing bolts from a lot of 20, containing one defective D, until D is drawn, one at a time and assuming sampling without replacement, that is, bolts drawn are not returned to the lot.
Choosing a committee of 3 from a group of 5 peopleGraph a sample space for the experiments
In Prob. 3, circle and mark the events A: Equal faces, B: Sum exceeds 9, C: Sum equals 7.
Answer the question in Prob. 11 for rolling 3 dice.

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