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mathematics
statistics

Questions and Answers of Statistics

In Example 9-6 we described how the “spring-like effect” in a golf club could be determined by measuring the coefficient of restitution (the ratio of the outbound velocity to the inbound velocity
Consider the shear strength experiment described in Example 10-9. Construct a 95% confidence interval on the difference in mean shear strength for the two methods. Is the result you obtained
Reconsider the shear strength experiment described in Example 10-9. Do each of the individual shear strengths have to be normally distributed for the paired t-test to be appropriate, or is it only
Consider the parking data in Example 10-10. Use the paired t-test to investigate the claim that the two types of cars have different levels of difficulty to parallel park use a = 0.10. Compare your
Reconsider the parking data in Example 10-10. Investigate the assumption that the differences in parking times are normally distributed.
The manager of a fleet of automobiles is testing two brands of radial tires and assigns one tire of each brand at random to the two rear wheels of eight cars and runs the cars until the tires wear
A computer scientist is investigating the usefulness of two different design languages in improving programming tasks. Twelve expert programmers, familiar with both languages, are asked to code a
Fifteen adult males between the ages of 35 and 50 participated in a study to evaluate the effect of diet and exercise on blood cholesterol levels. The total cholesterol was measured in each subject
An article in the Journal of Aircraft (Vol. 23, 1986, pp. 859€“864) describes a new equivalent plate analysis method formulation that is capable of modeling aircraft structures such as
Ten individuals have participated in a diet-modification program to stimulate weight loss. Their weight both before and after participation in the program is shown in the following list is there
Two different analytical tests can be used to determine the impurity level in steel alloys. Eight specimens are tested using both procedures, and the results are shown in the following tabulation. Is
Consider the weight-loss data in Exercise 10-41. Is there evidence to support the claim that this particular diet modification program will result in a mean weight loss of at least 10 pounds? Use a =
Consider the weight-loss experiment in Exercise 10-41. Suppose that, if the diet-modification program results in mean weight loss of at least 10 pounds, it is important to detect this with
For an F distribution, find the following:(a) f0.25,5,10 (b) f0.10,24,9(c) f0.05,8,15 (d) f0.75,5,10(e) f0.90,24,9 (f ) f0.95,8,15
For an F distribution, find the following:(a) f0.25,7,15 (b) f0.10,10,12(c) f0.01,20,10 (d) f0.75,7,15(e) f0.90,10,12 (f) f0.99,20,10
Two chemical companies can supply a raw material. The concentration of a particular element in this material is important. The mean concentration for both suppliers is the same, but we suspect that
Consider the etch rate data in Exercise 10-21. Test the hypothesis H0: σ2/1 = σ2/2 against H1: σ2/1  σ2/2 using a = 0.05, and draw conclusions.
Consider the etch rate data in Exercise 10-21. Suppose that if one population variance is twice as large as the other, we want to detect this with probability at least 0.90 (using a = 0.05). Are the
Consider the diameter data in Exercise 10-17. Construct the following: (a) A 90% two-sided confidence interval on σ1/ σ 2 (b) A 95% two-sided confidence interval on σ1/ σ2.
Consider the foam data in Exercise 10-18. Construct the following: (a) A 90% two-sided confidence interval on σ2/1 σ2/2 (b) A 95% two-sided confidence interval on σ2/1 σ2/2.
Consider the film speed data in Exercise 10-24. Test H0: σ2/1 = σ2/2 versus using a = 0.02.
Consider the gear impact strength data in Exercise 10-22. Is there sufficient evidence to conclude that the variance of impact strength is different for the two suppliers? Use a = 0.05.
Consider the melting point data in Exercise 10-25. Do the sample data support a claim that both alloys have the same variance of melting point? Use a = 0.05 in reaching your conclusion.
Exercise 10-28 presented measurements of plastic coating thickness at two different application temperatures. Test H0: σ2/1 = σ2/2 against H1: σ2/1  σ2/2 using a = 0.01.
A study was performed to determine whether men and women differ in their repeatability in assembling components on printed circuit boards. Random samples of 25 men and 21 women were selected, and
Reconsider the assembly repeatability experiment described in Exercise 10-56. Find a 98% confidence interval on the ratio of the two variances. Provide an interpretation of the interval.
Reconsider the film speed experiment in Exercise 10-24. Suppose that one population standard deviation is 50% larger than the other. Is the sample size n1 = n2 = 8 adequate to detect this difference
Reconsider the overall distance data for golf balls in Exercise 10-31. Is there evidence to support the claim that the standard deviation of overall distance is the same for both brands of balls (use
Reconsider the coefficient of restitution data in Exercise 10-32. Do the data suggest that the standard deviation is the same for both brands of drivers (use a = 0.05)? Explain how to answer this
Two different types of injection-molding machines are used to form plastic parts. A part is considered defective if it has excessive shrinkage or is discolored. Two random samples, each of size 300,
Two different types of polishing solution are being evaluated for possible use in a tumble-polish operation for manufacturing interocular lenses used in the human eye following cataract surgery.
Consider the situation described in Exercise 10-61. Suppose that p1 = 0.05 and p2 = 0.01.(a) With the sample sizes given here, what is the power of the test for this two-sided alternate?(b) Determine
Consider the situation described in Exercise 10-61. Suppose that p1 = 0.05 and p2 = 0.02.(a) With the sample sizes given here, what is the power of the test for this two-sided alternate?(b) Determine
A random sample of 500 adult residents of Maricopa County found that 385 were in favor of increasing the highway speed limit to 75 mph, while another sample of 400 adult residents of Pima County
Construct a 95% confidence interval on the difference in the two fractions defective for Exercise 10-61.
Construct a 95% confidence interval on the difference in the two proportions for Exercise 10-65. Provide a practical interpretation of this interval.
A procurement specialist has purchased 25 resistors from vendor 1 and 35 resistors from vendor 2. Each resistor€™s resistance is measured with the following results:(a) What distributional
An article in the Journal of Materials Engineering (1989, Vol. 11, No. 4, pp. 275–282) reported the results of an experiment to determine failure mechanisms for plasma sprayed thermal barrier
Consider Supplemental Exercise 10-69. (a) Construct a 95% confidence interval on the ratio of the variances σ1/ σ2, of failure stress under the two different test conditions. (b) Use
A liquid dietary product implies in its advertising that use of the product for one month results in an average weight loss of at least 3 pounds. Eight subjects use the product for one month, and the
The breaking strength of yarn supplied by two manufacturers is being investigated. We know from experience with the manufacturers’ processes that σ1 = 5 psi and σ2 = 4 psi. A random
The Salk polio vaccine experiment in 1954 focused on the effectiveness of the vaccine in combating paralytic polio. Because it was felt that without a control group of children there would be no
Consider Supplemental Exercise 10-72. Suppose that prior to collecting the data, you decide that you want the error in estimating σ1 = σ2 by x1 = x2 to be less than 1.5 psi. Specify the
A random sample of 1500 residential telephones in Phoenix in 1990 found that 387 of the numbers were unlisted. x2 x1 = 88 = 91A random sample in the same year of 1200 telephones in Scottsdale found
In a random sample of 200 Phoenix residents who drive a domestic car, 165 reported wearing their seat belt regularly, while another sample of 250 Phoenix residents who drive a foreign car revealed
Consider the previous exercise, which summarized data collected from drivers about their seat belt usage.(a) Do you think there is a reason not to believe these data? Explain your answer.(b) Is it
Consider the situation described in Exercise 10-62.(a) Redefine the parameters of interest to be the proportion of lenses that are unsatisfactory following tumble polishing with polishing fluids 1 or
Consider the situation of Exercise 10-62, and recall that the hypotheses of interest are H0: p1 = p2 versus H1: p1 ( p2.We wish to use a = 0.01. Suppose that if p1 = 0.9 and p2 = 0.6, we wish to
A manufacturer of a new pain relief tablet would like to demonstrate that its product works twice as fast as the competitor€™s product. Specifically, the manufacturer would like to
Suppose that we are testing H0: μ1 = μ2 versus H1: μ1  μ2 and we plan to use equal sample sizes from the two populations. Both populations are assumed to be normal with
Consider the fire-fighting foam expanding agents investigated in Exercise 10-18, in which five observations of each agent were recorded. Suppose that, if agent 1 produces a mean expansion that
A fuel-economy study was conducted for two German automobiles, Mercedes and Volkswagen. One vehicle of each brand was selected, and the mileage performance was observed for 10 tanks of fuel in each
Reconsider the fuel-economy study in Supplemental Exercise 10-83. Rework part (d) of this problem using an appropriate hypothesis-testing procedure. Did you get the same answer as you did originally?
An experiment was conducted to compare the filling capability of packaging equipment at two different wineries. Ten bottles of pinot noir from Ridgecrest Vineyards were randomly selected and
Consider Supplemental Exercise 10-85. Suppose that the true difference in mean fill volume is as much as 2 fluid ounces; did the sample sizes of 10 from each vineyard provide good detection
A Rockwell hardness-testing machine presses a tip into a test coupon and uses the depth of the resulting depression to indicate hardness. Two different tips are being compared to determine whether
Two different gauges can be used to measure the depth of bath material in a Hall cell used in smelting aluminum. Each gauge is used once in 15 cells by the same operator.(a) State any assumptions
An article in the Journal of the Environmental Engineering Division (“Distribution of Toxic Substances in Rivers,” 1982, Vol. 108, pp. 639–649) investigates the concentration of several
An article in Concrete Research (“Near Surface Characteristics of Concrete: Intrinsic Permeability,” Vol. 41, 1989), presented data on compressive strength x and intrinsic permeability y of
Regression methods were used to analyze the data from a study investigating the relationship between roadway surface temperature (x) and pavement deflection (y). Summary quantities were n = 20,
Consider the regression model developed in Exercise 11-2.(a) Suppose that temperature is measured in oC rather than oF. Write the new regression model that result.(b) What change in expected pavement
Montgomery, Peck, and Vining (2001) present data concerning the performance of the 28 National Football League teams in 1976. It is suspected that the number of games won (y) is related to the number
An article in Techno metrics by S. C. Narula and J. F. Wellington (€œPrediction, Linear Regression, and a Minimum Sum of Relative Errors,€ Vol. 19, 1977) presents data on the
The number of pounds of steam used per month by a chemical plant is thought to be related to the average ambient temperature (inoF) for that month. The past year€™s usage and temperature
The data shown in the following table are highway gasoline mileage performance and engine displacement for a sample of 20 cars.(a) Fit a simple linear model relating highway miles per gallon (y) to
An article in the Tappi Journal (March, 1986) presented data on green liquor Na2S concentration (in grams per liter) and paper machine production (in tons per day) Te data read from a graph) are
An article in the Journal of Sound and Vibration (Vol. 151, 1991, pp. 383€“394) described a study investigating the relationship between noise exposure and hypertension. The following data
An article in Wear (Vol. 152, 1992, pp. 171€“181) presents data on the fretting wear of mild steel and oil viscosity. Representative data follow, with x = oil viscosity and y = wear ear
An article in the Journal of Environmental Engineering (Vol. 115, No. 3, 1989, pp. 608€“619) reported the results of a study on the occurrence of sodium and chloride in surface streams in
A rocket motor is manufactured by bonding together two types of propellants, an igniter and a sustainer. The shear strength of the bond y is thought to be a linear function of the age of the
Show that in a simple linear regression model the point (x, y) lies exactly on the least squares regression line.
Consider the simple linear regression model Y =B0 + B1x + e suppose that the analyst wants to use z = x – x as the regress or variable.(a) Using the data in Exercise 11-12, construct one scatter
Suppose we wish to fit the model y*I = B*0 + B*1 (xi – x) +E, where y*i = yi, y (i = 1, 2, .., p , n). Find the least squares estimates of B*0 and B*1. How do they relate to B0 and B1?
Suppose we wish to fit a regression model for which the true regression line passes through the point (0, 0). The appropriate model is Y = Bx = E. Assume that we have n pairs of data (x1, y1), (x2,
Using the results of Exercise 11-16, fit the model Y = Bx + E to the chloride concentration-roadway area data in Exercise 11-11. Plot the fitted model on a scatter diagram of the data and comment on
Consider the data from Exercise 11-1 on x = compressive strength and y = intrinsic permeability of concrete. (a) Test for significance of regression using a = 0.05. Find the P-value for this test.
Consider the data from Exercise 11-2 on x = roadway surface temperature and y = pavement deflection.(a) Test for significance of regression using a = 0.05. Find the P-value for this test. What
Consider the National Football League data in Exercise 11-4.(a) Test for significance of regression using a = 0.01. Find the P-value for this test. What conclusions can you draw?(b) Estimate the
Consider the data from Exercise 11-5 on y = sales price and x = taxes paid.(a) Test H0: B1 = 0 using the t-test; use a = 0.05.(b) Test H0: B1 = 0 using the analysis of variance with a = 0.05. Discuss
Consider the data from Exercise 11-6 on y = steam usage and x = average temperature.(a) Test for significance of regression using a = 0.01. What is the P-value for this test? State the conclusions
Exercise 11-7 gave 20 observations on y = highway gasoline mileage and x = engine displacement.(a) Test for significance of regression using a = 0.01. Find the P-value for this test. What conclusions
Exercise 11-8 gave 13 observations on y = green liquor Na2S concentration and x = production in a paper mill.(a) Test for significance of regression using a = 0.05. Find the P-value for this test.
Exercise 11-9 presented data on y = blood pressure rise and x = sound pressure level.(a) Test for significance of regression using a = 0.05. What is the P-value for this test?(b) Estimate the
Exercise 11-11 presented data on y = chloride concentration in surface streams and x = roadway area.(a) Test the hypothesis H0: B1 = 0 versus H1: B1 = 0 using the analysis of variance procedure with
Refer to Exercise 11-12, which gives 20 observations on y = shear strength of a propellant and x = propellant age.(a) Test for significance of regression with a = 0.01. Find the P-value for this
Suppose that each value of xi is multiplied by a positive constant a, and each value of yi is multiplied by another positive constant b. Show that the t-statistic for testing H0: B1 = 0 versus H1: B1
Consider the no-intercept model Y = Bx + E with the E’s NID (0, σ2). The estimate of σ2 is s2 Σ = (yi – Bxi) 2 / (n – 1) and v(B) = σ2 / Σ= 1x2/i (a) Devise a test
The type II error probability for the t-test for H0: B1 = B1, 0 can be computed in a similar manner to the t-tests of Chapter 9. If the true value of B1 is B1, the value =|B1, 0 –
Refer to the data in Exercise 11-1 on y = intrinsic permeability of concrete and x = compressive strength. Find a 95% confidence interval on each of the following: (a) Slope (b) Intercept(c) Mean
Exercise 11-2 presented data on roadway surface temperature x and pavement deflection y. Find a 99% confidence interval on each of the following:(a) Slope (b) Intercept(c) Mean deflection when
Exercise 11-4 presented data on the number of games won by NFL teams in 1976. Find a 95% confidence interval on each of the following:(a) Slope (b) Intercept(c) Mean number of games won when
Refer to the data on y = house selling price and x = taxes paid in Exercise 11-5. Find a 95% confidence interval on each of the following:(a) B1 (b) B0(c) Mean selling price when the taxes paid are x
Exercise 11-6 presented data on y = steam usage and x = monthly average temperature.(a) Find a 99% confidence interval for B1.(b) Find a 99% confidence interval for B0.(c) Find a 95% confidence
Exercise 11-7 presented gasoline mileage performance for 20 cars, along with information about the engine displacement. Find a 95% confidence interval on each of the following:(a) Slope (b)
Consider the data in Exercise 11-8 on y = green liquor Na2S concentration and x = production in a paper mill. Find a 99% confidence interval on each of the following:(a) B1 (b) B0(c) Mean Na2S
Exercise 11-9 presented data on y = blood pressure rise and x = sound pressure level. Find a 95% confidence interval on each of the following:(a) B1 (b) B0(c) Mean blood pressure rise when the sound
Refer to the data in Exercise 11-10 on y = wear volume of mild steel and x = oil viscosity. Find a 95% confidence interval on each of the following: (a) Intercept (b) Slope(c) Mean wear when oil
Exercise 11-11 presented data on chloride concentration y and roadway area x on watersheds in central Rhode Island. Find a 99% confidence interval on each of the following:(a) B1 (b) B0(c) Mean
Refer to the data in Exercise 11-12 on rocket motor shear strength y and propellant age x. Find a 95% confidence interval on each of the following:(a) Slope B1 (b) Intercept B0(c) Mean shear strength
Refer to the NFL team performance data in Exercise 11-4.(a) Calculate R2 for this model and provide a practical interpretation of this quantity.(b) Prepare a normal probability plot of the residuals

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