New Semester Started Get 50% OFF Study Help! --h --m --s Claim Now

Question Answers

Textbooks

Find textbooks, questions and answers

Oops, something went wrong!

Change your search query and then try again

Result Not Found

Books FREE
Study Help
Tutors
AI Study Planner NEW
Sell Books

Search
Sign In
Register

study help
mathematics
statistics

John E Freunds Mathematical Statistics With Applications 8th Edition Irwin Miller, Marylees Miller - Solutions

In a random sample, s = 2.53 minutes for the amount of time that 30 women took to complete the writ-ten test for their driver’s licenses. At the 0.05 level of significance, test the null hypothesis σ = 2.85 minutes against the alternative hypothesis σ < 2.85 minutes. (Use the method described
With reference to Exercise 13.4, find the required size of the samples when σ1 = 9, σ2 = 13, ∂ = 80, ∂t = 86, α = 0.01, and β = 0.01.
Use the method of Exercise 13.7 to rework Exercise 13.49. In exercise In a random sample, s = 2.53 minutes for the amount of time that 30 women took to complete the writ-ten test for their driver’s licenses. At the 0.05 level of significance, test the null hypothesis σ = 2.85 minutes against the
Past data indicate that the standard deviation of measurements made on sheet metal stampings by experienced inspectors is 0.41 square inch. If a new inspector measures 50 stampings with a standard deviation of 0.49 square inch, use the method of Exercise 13.7 to test the null hypothesis σ = 0.41
With reference to Example 13.5, test the null hypothesis σ1 – σ2 = 0 against the alternative hypothesis σ1 – σ2 > 0 at the 0.05 level of significance.
With reference to Exercise 13.40, test at the 0.10 level of significance whether it is reasonable to assume that the two populations sampled have equal variances. In Exercise To find out whether the inhabitants of two South Pacific islands may be regarded as having the same racial ancestry, an
With reference to Exercise 13.42, test at the 0.02 level of significance whether it is reasonable to assume that the two populations sampled have equal variances.In exerciseTo compare two kinds of front- end designs, six of each kind were installed on a certain make of compact car. Then each car
With reference to Example 13.8, show that the critical region is x ≤ 5 or x ≥ 15 and that, corresponding to this critical region, the level of significance is actually 0.0414. Example 13.8 If x = 4 of n = 20 patients suffered serious side effects from a new medication, test the null hypothesis
It has been claimed that more than 40 percent of all shoppers can identify a highly advertised trademark. If, in a random sample, 10 of 18 shoppers were able to identify the trademark, test at the 0.05 level of significance whether the null hypothesis θ = 0.40 can be rejected against the
With reference to Exercise 13.57, find the critical region and the actual level of significance corresponding to this critical region. In exercise It has been claimed that more than 40 percent of all shoppers can identify a highly advertised trademark. If, in a random sample, 10 of 18 shoppers
A doctor claims that less than 30 percent of all per-sons exposed to a certain amount of radiation will feel any ill effects. If, in a random sample, only 1 of 19 per-sons exposed to such radiation felt any ill effects, test the null hypothesis θ = 0.30 against the alternative hypothesis θ < 0.30
Making use of the fact that the chi-square distribution can be approximated with a normal distribution when v, the number of degrees of freedom, is large, show that for large samples from normal populationsIs an approximate critical region of size a for testing the null hypothesis Ïƒ2 =
In a random sample, 12 of 14 industrial accidents were due to unsafe working conditions. Use the 0.01 level of significance to test the null hypothesis θ = 0.40 against the alternative hypothesis θ ≠ 0.40.
With reference to Exercise 13.61, find the critical region and the actual level of significance corresponding to this critical region. In exercise In a random sample, 12 of 14 industrial accidents were due to unsafe working conditions. Use the 0.01 level of significance to test the null hypothesis
In a random survey of 1,000 households in the United States, it is found that 29 percent of the house-holds contained at least one member with a college degree. Does this finding refute the statement that the proportion of all such U.S. households is at least 35 percent? (Use the 0.05 level of
In a random sample of 12 undergraduate business students, 6 said that they will take advanced work in accounting. Use the 0.01 level of significance to test the null hypothesis θ = 0.20, that is, 20 percent of all under-graduate business students will take advanced work in accounting, against the
A food processor wants to know whether the probability is really 0.60 that a customer will prefer a new kind of packaging to the old kind. If, in a random sample, 7 of 18 customers prefer the new kind of packaging to the old kind, test the null hypothesis θ = 0.60 against the alter-native
In a random sample of 600 cars making a right turn at a certain intersection, 157 pulled into the wrong lane. Use the 0.05 level of significance to test the null hypothesis that the actual proportion of drivers who make this mistake at the given intersection is θ = 0.30 against the alternative
The manufacturer of a spot remover claims that his product removes 90 percent of all spots. If, in a random sample, only 174 of 200 spots were removed with the manufacturer’s product, test the null hypothesis θ = 0.90 against the alternative hypothesis θ < 0.90 at the 0.05 level of significance.
In random samples, 74 of 250 persons who watched a certain television program on a small TV set and 92 of 250 persons who watched the same program on a large set remembered 2 hours later what products were advertised. Use the x2 statistic to test the null hypothesis θ1 = θ2 against the
Use the statistic of Exercise 13.12 to rework Exercise 13.68.In exerciseIn random samples, 74 of 250 persons who watched a certain television program on a small TV set and 92 of 250 persons who watched the same program on a large set remembered 2 hours later what products were advertised. Use the
Making use of the result of Exercise 8Î¸28 on page 250, show that for large random samples from normal populations, tests of the null hypothesis Ïƒ2 = Ïƒ20 can be based on the statisticWhich has approximately the standard normal distribution.
In random samples, 46 of 400 tulip bulbs from one nursery failed to bloom and 18 of 200 tulip bulbs from another nursery failed to bloom. Use the θ2 statistic to test the null hypothesis θ1 = θ2 against the alternative hypothesis θ1 ≠ θ2 at the 0.05 level of significance.
Use the statistic of Exercise 13.12 to rework Exercise 13.70, and verify that the square of the value obtained for z equals the value obtained for x2.In exerciseIn random samples, 46 of 400 tulip bulbs from one nursery failed to bloom and 18 of 200 tulip bulbs from another nursery failed to bloom.
In a random sample of 200 persons who skipped breakfast, 82 reported that they experienced midmorning fatigue, and in a random sample of 300 persons who ate breakfast, 87 reported that they experienced midmorning fatigue. Use the method of Exercise 13.12 and the 0.05 level of significance to test
If 26 of 200 tires of brand A failed to last 30,000 miles, whereas the corresponding figures for 200 tires of brands B, C, and D were 23, 15, and 32, test the null hypothesis that there is no difference in the durability of the four kinds of tires at the 0.05 level of significance.
In random samples of 250 persons with low incomes, 200 persons with average incomes, and 150 per-sons with high incomes, there were, respectively, 155, 118, and 87 who favor a certain piece of legislation. Use the 0.05 level of significance to test the null hypothesis θ1 = θ2 = θ3 (that the
Samples of an experimental material are produced by three different prototype processes and tested for compliance to a strength standard. If the tests showed the following results, can it be said at the 0.01 level of significance that the three processes have the same probability of passing this
In a study of parents€™ feelings about a required course in sex education, 360 parents, a random sample, are classified according to whether they have one, two, or three or more children in the school system and also whether they feel that the course is poor, adequate, or good. Based on
Tests of the fidelity and the selectivity of 190 radios produced the results shown in the following table:Use the 0.01 level of significance to test the null hypothesis that fidelity is independent of selectivity.
The following sample data pertain to the shipments received by a large firm from three different vendors:Test at the 0.01 level of significance whether the three vendors ship products of equal quality.
Analyze the 3 × 3 table on page 370, which pertains to the responses of shoppers in three different cities with regard to two detergents. Use the 0.05 level of significance.
Show that the two formulas for x2 on pages 368 and 369 are equivalent.
Four coins were tossed 160 times and 0, 1, 2, 3, or 4 heads showed, respectively, 19, 54, 58, 23, and 6 times. Use the 0.05 level of significance to test whether it is reasonable to suppose that the coins are balanced and randomly tossed.
It is desired to test whether the number of gamma rays emitted per second by a certain radioactive sub-stance is a random variable having the Poisson distribution with λ = 2.4. Use the following data obtained for 300 1-second intervals to test this null hypothesis at the 0.05 level of significance:
Each day, Monday through Saturday, a baker bakes three large chocolate cakes, and those not sold on the same day are given away to a food bank. Use the data shown in the following table to test at the 0.05 level of significance whether they may be looked upon as values of a binomial random variable:
The following is the distribution of the readings obtained with a Geiger counter of the number of particles emitted by a radioactive substance in 100 successive 40-second intervals:(a) Verify that the mean and the standard deviation of this distribution are x̅ = 20 and s = 5.(b) Find the
The following are the hours of operation to failure of 38 light bulbs.Use a suitable statistical computer program to test whether the mean failure time of such light bulbs is significantly less than 300 hours. Use the 0.01 level of significance.
The following are the hours of operation to failure of 38 light bulbs.Use a suitable statistical computer program to test whether the mean failure time of such light bulbs is significantly less than 300 hours. Use the 0.01 level of significance.
Samples of three materials under consideration for the housing of machinery on a seagoing vessel are tested by means of a salt-spray test. Any sample that leaks when subject to a power spray is considered to have failed. The following are the test results:Use a suitable statistical computer program
Modify the critical regions on pages 365 and 366 so that they can be used to test the null hypothesis λ = λ0 against the alternative hypotheses λ > λ0, λ < λ0, and λ ≠ λ0 on the basis of n observations. Here λ is the parameter of the Poisson distribution.
With reference to Example 14.1, show that the regression equation of X on Y isAlso sketch the regression curve. In Example 14.1
Show that if µY|x is linear in x and var(Y|x) is constant, then var(Y|x) = σ22 (1 – ρ2).
The following data represent more extended measurements of monthly water usage at the plant referred to in Exercise 14.98 over a period of 20 months:(a) Use an appropriate computer program to fit a linear surface to these data. (b) Use a computer program to make a normal-scores plot of the
Using the data of Exercise 14.99, In exercise(a) Create a new variable, x22. (b) Fit a surface of the form(c) Find the correlation matrix of the three independent variables. Is there evidence of multi-collinearity? (d) Standardize each of the independent variables, x1 and x2, and
Using the data of Exercise 14.100,In exercise(a) Create a new variable, x1x2. (b) Fit a surface of the form (c) Find the correlation matrix of the four independent variables. Is there evidence of multicollinearity? (d) Standardize each of the three independent variables x1, x2, and x3, and create
Given a pair of random variables X and Y having the variances σ21 and σ22 and the correlation coefficient ρ, use Theorem 4.14 to express var(X/s1 + Y/s2) and var(X/s1 – Y/s2) in terms of σ1, σ2, and ρ. Then, making use of the fact that variances cannot be negative, show that –1 ≤ ρ ≤
Given the random variables X1, X2, and X3 having the joint density f(x1, x2, x3), show that if the regression of X3 on X1 and X2 is linear and written asThen Where µi = E(Xi), Ïƒ2i = var(Xi), and Ïƒij = cov(Xi,Xj). [Proceed as on pages 386 and 387, multiplying by (x1
Find the least squares estimate of the parameter β in the regression equation µY|x = βx.
Solve the normal equations on page 390 simultaneously to show that
When the x€™s are equally spaced, the calculation of and can be simplified by coding the x€™s by assigning them the values . . . ,- 3,- 2,- 1, 0, 1, 2, 3, . . . when n is odd, or the values . . . ,- 5,- 3,- 1, 1, 3, 5, . . . when n is even. Show that with this coding the
The method of least squares can be used to fit curves to data. Using the method of least squares, find the normal equations that provide least squares estimates of a, β, and γ when fitting a quadratic curve of the form y = a + bx + γx2 to paired data.
Making use of the fact that = y €“ Î² and Î² Sxy/Sxx , show that
Show that (a) ∑2, the random variable corresponding to 2, is not an unbiased estimator of σ2; (b) S2e = n·∑2 / n–2 is an unbiased estimator of σ2. The quantity se is often referred to as the standard error of estimate.
Using se (see Exercise 14.18) instead of , rewrite (a) The expression for t in Theorem 14.4; (b) The confidence interval formula of Theorem 14.5. Exercise 14.18 Show that (a) ∑2, the random variable corresponding to 2, is not an unbiased estimator of σ2; (b) S2e = n·∑2 / n–2 is an
Given the joint destinyFind µY|x and µX|y.
Under the assumptions of normal regression analysis, show that(a) The least squares estimate of a in Theorem 14.2 can be written in the form(b) A has a normal distribution with
Use Theorem 4.15 show thatTheorem 4.15 If X1, X2, . . . , Xn are random variables and Where a1, a2, . . . , an, b1, b2, . . . , bn are constants, then
Use the result of part(b) of exercise 14.20 to show thatIs a value of a random variable having the standard normal distribution. Also, use the first part of Theorem 14.3 and the fact that A and nˆ‘2/Ïƒ2 are independent to show that Is a value of a random variable having the t
Use the results of Exercises 14.20 and 14.21 and the fact that E(BË†) = Î² and var(BË†) = Ïƒ2/ Sxx to show that YË†0 = AË† + BË† is a random variable having a normal distribution with the meanAnd the variance Also, use the first
Derive a (1 – α) 100% confidence interval for µY|x0, the mean of Y at x = x0, by solving the double inequality –tα/2,n–2 < t < tα/2, n–2 with t given by the formula of Exercise 14.23.
Use the results of Exercises 14.20 and 14.21 and the fact that E(BË†) = Î² and var(BË†) = Ïƒ2/ Sxx to show that Y0 €“ (AË† + BË†x0) is a random variable having a normal distribution with zero mean and the varianceHere Y0 has a
Solve the double inequality –tα/2,n–2 < t < tα/2,n–2 with t given by the formula of Exercise 14.25 so that the middle term is y0 and the two limits can be calculated without knowledge of y0. Although the resulting double inequality may be interpreted like a confidence interval, it is not
Verify that the formula for t of Theorem 14.4 can be written asTheorem 14.4 Under the assumptions of normal regression analysis, Is a value of a random variable having the t distribution with n €“ 2 degrees of freedom.
Use the formula for t of Exercise 14.28 to derive the following (1 €“ Î±) 100% confidence limits for Î²:In exercise
Given the joint destinyFind µY|x and µX|y.
Use the formula for t of Exercise 14.28 to show that if the assumptions underlying normal regression analysis are met and Î² = 0, then R2 has a beta distribution with the mean 1 / n €“ 1.In exercise
By solving the double inequality €“zÎ±/2 ‰¤ z ‰¤ zÎ±/2 (with z given by the formula on page 402) for Ï, derive a (1 €“ Î±) 100% confidence interval formula for Ï.On page
In a random sample of n pairs of values of X and Y, (xi, yj) occurs fij times for i = 1, 2, . . . , r and j = 1, 2, . . . , c. Letting fi, denote the number of pairs where X takes on the value xi and fj the number of pairs where Y takes on the value yj, write a formula for the coefficient of
If b is the column vector of the β’s, verify in matrix notation that q = (Y – Xb)'(Y – Xb) is a minimum when b = B = (X'X)–1(X'Y).
Verify that under the assumptions of normal multiple regression analysis(a) The maximum likelihood estimates of the Î²€™ s equal the corresponding least squares estimates;(b) The maximum likelihood estimate of s is
Use the t statistic of Theorem 14.8 to construct a (1 €“ Î±)100% confidence interval formula for Î²i for i = 0, 1, . . . , k.Theorem 14.8Under the assumptions of normal multiple regression analysis,Are values of random variables having the t distribution with n €“ k €“ 1 degrees of
If x01, x02, . . . , x0k are given values of x1, x2, . . . , xk and X0 is the column vectorIt can be shown that Is a value of a random variable having the t distribution with n- k- 1 degrees of freedom. (a) Show that for k = 1 this statistic is equivalent to the one of Exercise 14.23. (b) Derive
Given the joint densityShow that µY|x = 1 + 1/x and that var(Y|x) does not exist.
With x01, x02, . . . , x0k and X0 as defined in Exercise 14.39 and Y0 being a random variable that has a normal distribution with the mean Î²0 + Î²1x01 + · · · + Î²kx0k and the variance Ïƒ2, it can be shown thatIs a value of a random
The following data give the diffusion time (hours) of a silicon wafer used in manufacturing integrated circuits and the resulting sheet resistance of transfer:(a) Find the equation of the least squares line fit to these data. (b) Predict the sheet resistance when the diffusion time is 1.3 hours.
Various doses of a poisonous substance were given to groups of 25 mice and the following results were observed:(a) Find the equation of the least squares line fit to these data. (b) Estimate the number of deaths in a group of 25 mice that receive a 7-milligram dose of this poison.
The following are the scores that 12 students obtained on the midterm and final examinations in a course in statistics:(a) Find the equation of the least squares line that will enable us to predict a student€™s final examination score in this course on the basis of his or her score on the
Raw material used in the production of a synthetic fiber is stored in a place that has no humidity control. Measurements of the relative humidity and the moisture content of samples of the raw material (both in percent-ages) on 12 days yielded the following results:(a) Fit a least squares line that
The following data pertain to the chlorine residual in a swimming pool at various times after it has been treated with chemicals:(a) Fit a least squares line from which we can predict the chlorine residual in terms of the number of hours since the pool has been treated with chemicals. (b) Use the
Use the coding of Exercise 14.15 to rework both parts of Exercise 14.42.In exerciseWhen the x€™s are equally spaced, the calculation of and can be simplified by coding the x€™s by assigning them the values . . . ,- 3,- 2,- 1, 0, 1, 2, 3, . . . when n is odd, or the values . .
Use the coding of Exercise 14.15 to rework both parts of Exercise 14.45.In exerciseWhen the x€™s are equally spaced, the calculation of and can be simplified by coding the x€™s by assigning them the values . . . ,- 3,- 2,- 1, 0, 1, 2, 3, . . . when n is odd, or the values . .
During its first five years of operation, a company’s gross income from sales was 1.4, 2.1, 2.6, 3.5, and 3.7 million dollars. Use the coding of Exercise 14.15 to fit a least squares line and, assuming that the same linear trend continues, predict the company’s gross income from sales during
If a set of paired data gives the indication that the regression equation is of the form µY|x = α ∙ βx, it is customary to estimate a and β by fitting the lineto the points {(xi, logyi); i = 1, 2, . . . , n} by the method of least squares. Use this technique to fit an exponential curve of the
With reference to Exercise 3.70 on page 100, use the results of parts (c) and (d) to find µX|1 and µY|0.
If a set of paired data gives the indication that the regression equation is of the form µY|x = Î± ˆ™ xÎ²^, it is customary to estimate a and Î² by fitting the lineTo the points {(log xi, logyi); i = 1, 2, . . . , n} by the method of least squares.
With reference to Exercise 14.42, test the null hypothesis Î² = 1.25 against the alternative hypothesis Î² > 1.25 at the 0.01 level of significance.In exerciseVarious doses of a poisonous substance were given to groups of 25 mice and the following results were observed:(a)
With reference to Exercise 14.44, test the null hypothesis Î² = 0.350 against the alternative hypothesis Î² In exerciseRaw material used in the production of a synthetic fiber is stored in a place that has no humidity control. Measurements of the relative humidity and the
The following table shows the assessed values and the selling prices of eight houses, constituting a random sample of all the houses sold recently in a metropolitan area:(a) Fit a least squares line that will enable us to predict the selling price of a house in that metropolitan area in terms of
With reference to Exercise 14.43, construct a 99% confidence interval for the regression coefficient β. In exerciseThe following are the scores that 12 students obtained on the midterm and final examinations in a course in statistics:(a) Find the equation of the least squares line that will
With reference to Exercise 14.45, construct a 98% confidence interval for the regression coefficient Î².In exerciseThe following data pertain to the chlorine residual in a swimming pool at various times after it has been treated with chemicals:(a) Fit a least squares line from which we
With reference to Example 14.4, use the theory of Exercise 14.22 to test the null hypothesis Î± = 21.50 against the alternative hypothesis Î± ‰ 21.50 at the 0.01 level of significance.In exerciseUse the result of part(b) of exercise 14.20 to show thatIs a value
The following data show the advertising expenses (expressed as a percentage of total expenses) and the net operating profits (expressed as a percentage of total sales) in a random sample of six drugstores:(a) Fit a least squares line that will enable us to predict net operating profits in terms of
With reference to Exercise 14.42, use the theory of Exercise 14.22 to construct a 95% confidence interval for a.In exerciseUse the result of part(b) of exercise 14.20 to show thatIs a value of a random variable having the standard normal distribution. Also, use the first part of Theorem 14.3 and
With reference to Exercise 14.43, use the theory of Exercise 14.22 to construct a 99% confidence interval for a.In exerciseUse the result of part(b) of exercise 14.20 to show thatIs a value of a random variable having the standard normal distribution. Also, use the first part of Theorem 14.3 and
With reference to Exercise 3.71 on page 100, find an expression for µY|x.
Use the theory of Exercises 14.24 and 14.26, as well as the quantities already calculated in Examples 14.4 and 14.5, to construct (a) A 95% confidence interval for the mean test score of persons who have studied 14 hours for the test; (b) 95% limits of prediction for the test score of a person
Use the theory of Exercises 14.24 and 14.26, as well as the quantities already calculated in Exercise 14.51 for the data of Exercise 14.42, to find (a) A 99% confidence interval for the expected number of deaths in a group of 25 mice when the dosage is 9 milligrams; (b) 99% limits of prediction
Redo Exercise 14.61 when the dosage is 20 milligrams. Note the greatly increased width of the confidence limits for the expected number of deaths and of the limits of prediction. This example illustrates that extrapolation, estimating a value of Y for observations outside the range of the data,
The following table shows the elongation (in thousandths of an inch) of steel rods of nominally the same composition and diameter when subjected to various tensile forces (in thousands of pounds).(a) Use appropriate computer software to fit a straight line to these data. (b) Construct 99%

Showing 40000 - 40100 of 88243

First
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
Last

Step by Step Answers

Services

Sitemap
Fun
Definitions
Become Tutor
Used Textbooks
Study Help Categories
Recent Questions
Expert Questions
Campus Wear
Sell Your Books

Company Info

Security
Copyrights
Privacy Policy
Terms & Conditions
SolutionInn Fee
Scholarship
Online Quiz
Give Feedback, Get Rewards

Get In Touch

About Us
Contact Us
Career
Jobs
FAQ
Student Discount
Campus Ambassador

Secure Payment

Download Our App

© 2026 SolutionInn. All Rights Reserved