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

The following are loads (grams) put on the centers of like plastic rods with the resulting deflections (cm).(a) Use an appropriate computer program to fit a straight line to these data. (b) Using the 0.95 level of significance, test the null hypothesis that Î² = 0.01 against the
An achievement test is said to be reliable if a student who takes the test several times will consistently get high (or low) scores. One way of checking the reliability of a test is to divide it into two parts, usually the even-numbered problems and the odd- numbered problems, and observe the
With reference to Exercise 14.65, use the formula obtained in Exercise 14.31 to construct a 95% confidence interval for Ï.In ExerciseFormula
The following data pertain to x, the amount of fertilizer (in pounds) that a farmer applies to his soil, and y, his yield of wheat (in bushels per acre):Assuming that the data can be looked upon as a random sample from a bivariate normal population, calculate r and test its significance at the 0.01
With reference to Exercise 14.67, use the formula obtained in Exercise 14.31 to construct a 99% confidence interval for Ï.In exerciseFormula
Use the formula of Exercise 14.29 to calculate a 95% confidence interval for β for the numbers of hours studied and the test scores on page 388 and compare this interval with the one obtained in Example 14.6.
Given the joint densityShow that (a) µY|x = x/2 and µX|y = 1+y / 2; (b) E(XmYn) = 2 / (n + 1)(m + n + 2). Also, (c) verify the results of part (a) by substituting the values of µ1, µ2, Ïƒ1, Ïƒ2, and Ï, obtained with the formula of part (b),
The calculation of r can often be simplified by adding the same constant to each x, adding the same constant to each y, or multiplying each x and/or y by the same positive constants. Recalculate r for the data of Example 14.7 by first multiplying each x and each y by 10 and then subtracting 70 from
The table at the bottom of the page shows how the history and economics scores of 25 students are distributed. Use the method of Exercise 14.32 to determine the value of r, replacing the row headings by the corresponding class marks (midpoints) 23, 28, 33, 38, 43, and 48 and the column headings by
Rework Exercise 14.71, coding the class marks of the history scores €“2, €“1, 0, 1, and 2 and the class marks of the economics scores €“2, €“1, 0, 1, 2, and 3. (It follows from Exercise 14.70 that this kind of coding will not affect the value of r.)In
If the row categories as well as the column categories of an r × c table are ordered, we can replace the row headings and also the column headings by consecutive integers and then calculate r with the formula obtained in Exercise 14.32. Use this method to rework Example 13.11 on page 372,
With reference to the r Ã— c table on page 371, use the method suggested in Exercise 14.73 to test at the 0.05 level of significance whether there is a relationship between I.Q. and on- the- job performance. Replace the row headings as well as the column headings by - 1, 0, and 1.r
(a) Use an appropriate computer program to obtain the sample correlation coefficient for the data of Exercise 14.63. (b) Test whether r is significantly different from 0 using the 0.05 level.
(a) Use an appropriate computer program to obtain the sample correlation coefficient for the data of Exercise 14.64. (b) Test whether this coefficient is significant using the 0.10 level.
The following are sample data provided by a moving company on the weights of six shipments, the distances they were moved, and the damage that was incurred:(a) Assuming that the regression is linear, estimate Î²0, Î²1, and Î²2. (b) Use the results of part (a) to
Given the joint densityShow that µY|x = 23(1 €“ x) and verify this result by deter-mining the values of µ1, µ2, s1, s2, and Ï and by substituting them into the first formula of Theorem 14.1.
The following data were collected to determine the relationship between two processing variables and the hardness of a certain kind of steel:Fit a plane by the method of least squares, and use it to estimate the average hardness of this kind of steel when the copper content is 0.14 percent and the
When the x1’s, x2’s, . . . , and/or the xk’s are equally spaced, the calculation of the β^’s can be simplified by using the coding suggested in Exercise 14.15. Rework Exercise 14.80 coding the x1-values – 1, 0, and 1 and the x2-values –1 and 1. (For the coded x1’s and x2’s, call
The regression models that we introduced in Sections 14.2 and 14.6 are linear in the x€™s, but, more important, they are also linear in the Î²€™s. Indeed, they can be used in some problems where the relationship between the x€™s and y is not linear. For
Given the joint densityShow that the random variables X and Y are uncorrelated but not independent.
Use an appropriate computer program to redo Exercise 14.82 without coding the x-values.
(a) Use an appropriate computer program to fit a plane to the following data relating the monthly water usage of a production plant (gallons) to its monthly production (tons), mean monthly ambient temperature (°F), and the monthly number of days of plant operation over a period of 12 months.(b)
(a) Fit a linear surface to the following data:(b) How good a fit is obtained? (c) Plot the residuals against and determine whether the pattern is €œrandom.€ (d) Check for multicollinearity among the independent variables.
For the one-way analysis of variance with a independent samples of size n, show that
Prove Theorem 15.4.Theorem 15.4Where T·j is the total of the values obtained for the jth block, T.. is the grand total of all nk observations, and Is the correction term.
Prove the statement made on page 436; that
Fill in the details of the Proof of Theorem 15.5.Theorem 15.5Where i.. is the mean of the observations of the ith value of the first treatment, ·j· is the mean of the jth value of the second treatment, ..k is the mean of the kth replicate, ij· is the mean of the ith and jth
Prove Theorem 15.6.Theorem 15.6Where Ti.., T·j· , and T..k are the totals of the values obtained for treatment A, treatment B, and the replicates, respectively, and Tij· is the sum over replicates obtained for values corresponding to the combination of treatment A at level i
Prove the result given on page 444 for the analysis of the Latin-square experiment.
Develop the analysis-of-variance table for a Latin-square experiment.
To compare the effectiveness of three different types of phosphorescent coatings on airplane instrument dials, eight dials each are coated with the three types. Then the dials are illuminated by an ultraviolet light, and the following are the number of minutes each glowed after the light source was
The following are the numbers of mistakes made in five successive weeks by four technicians working for a medical laboratory:Test at the 0.05 level of significance whether the differences among the four sample means can be attributed to chance.
Three groups of six guinea pigs each were injected, respectively, with 0.5 milligram, 1.0 milligram, and 1.5 milligrams of a new tranquilizer, and the following are the numbers of minutes it took them to fall asleep:Test at the 0.05 level of significance whether the null hypothesis that differences
The following are the numbers of words per minute that a secretary typed on several occasions on four different typewriters:Use the computing formulas of Exercise 15.4 to calculate the sums of squares required to test at the 0.05 level of significance whether the differences among the four sample
Prove Theorem 15.2.Theorem15.2And Where Ti· is the total of the values obtained for the ith treatment and T.. is the grand total of all a ˆ™ n observations. The quantity Is called the correction term.
A consumer testing service, wishing to test the accuracy of the thermostats of three different kinds of electric irons, set them at 480°F and obtained the following actual temperature readings by means of a thermocouple:Use the computing formulas of Exercise 15.4 to calculate the sums of
In Section 13.7 we pointed out that in the chi-square analysis of an r × c table we do not take into account a possible ordering of the rows and/or columns. When the rows and the columns are both ordered, we indicated an alternative to the chi-square analysis in Exercises 14.73 and 14.74 on page
Use the method of Exercise 15.21 to analyze the 3 × 3 table of Exercise 13.78 on page 380, and compare the result with the result obtained in that exercise.
An experiment was performed to judge the effect of four different fuels and three different types of launchers on the range of a certain rocket. Test, on the basis of the following ranges in miles, whether there is a significant effect due to differences in fuels and whether there is a significant
The following are the cholesterol contents in milligrams per package that four laboratories obtained for 6- ounce packages of three very similar diet foods:Perform a two- way analysis of variance and test the null hypotheses concerning the diet foods and the laboratories at the 0.05 level of
A laboratory technician measures the breaking strength of each of five kinds of linen threads by using four different measuring instruments, I1, I2, I3 and I4, and obtains the following results, in ounces:Perform a two- way analysis of variance, using the 0.05 level of significance for both tests.
Among the nine persons interviewed in a poll, three are Easterners, three are Southerners, and three are Westerners. By profession, three of them are teachers, three are lawyers, and three are doctors, and no two of the same profession come from the same part of the United States. Also, three are
The experiment described in Exercise 15.23 was repeated, with the following results.Combining these data with those of Exercise 15.23, perform an appropriate analysis of variance to test the null hypotheses involving fuels, launchers, replicates, and the fuel€“launcher interaction. Use
The experiment described in Exercise 15.24 was repeated, with the following results.Combining these data with those of Exercise 15.24, perform an appropriate analysis of variance to test the null hypotheses involving diet foods, laboratories, replicates, and the food-laboratory interaction. Use the
Using the data of the example on page 445 and an appropriate computer, program, find the mean values of each level of operator, bonder, and replicate, also find the means required to examine the interaction between operators and bonders.
If, in a one-way analysis of variance, the sample sizes are unequal and there are ni observations for the ith treatment, show thatIs analogous to the identity of Theorem 15.1. Also show that the degrees of freedom for SST, SS(Tr), and SSE are, respectively, N €“ 1, a €“ 1, and N
An index of flavor was used to evaluate the effect of adding dioctyl sodium sulfosuccinate (DSS) to milk to stabilize its flavor. Four DSS levels (in parts per million) were used, including no DSS, and the milk was stored for 7 weeks and 28 weeks to observe the effect of DSS level on storage time.
Perform a multiple-range test to determine the nature of the differences among the three detergents in Example 15.1. Use the 0.01 level of significance.
Perform a multiple-range test to determine the nature of the block differences in Example 15.2. Use the 0.05 level of significance.
Perform multiple-range tests to characterize the differences among compressor designs and among regions in Example 15.3. Use the 0.05 level of significance.
Perform appropriate multiple- range tests, using the 0.05 level of significance, to characterize the differences among the diet-food means and the laboratory means in Exercise 15.28. Under what circumstances would it not be appropriate to make such a test?
Perform appropriate multiple- range tests, using the 0.01 level of significance, to characterize the differences among the launcher means and the fuel means in Exercise 15.27. Under what circumstances would it not be appropriate to make such a test?
Perform appropriate multiple-range tests, using the 0.05 level of significance, to characterize the differences among the DSS-level means and the storage- time means in Exercise 15.30.
Perform appropriate multiple- range tests, using the 0.05 level of significance, to characterize the differences among the bonder means and the operator means found in Exercise 15.29.
The sample data in the following Latin square are the scores obtained by nine college students of various ethnic backgrounds and various professional interests in an American history test:In this table, A, B, and C are the three instructors by whom the nine college students were taught the course
(a) Perform an analysis of variance of the data of the following Latin- square experiment. In this experiment, the treatments, represented by A, B, and C, are three different kinds of golf balls; each is struck by three different golf clubs, K1, K2, and K3, by each of three different golf
With reference to Exercise 15.3, show that the computing formulas for the sums of squares areAnd
A Latin-square experiment was performed to compare the solder-bond strength of a tin-can body (in pounds force required to break the bond). Five different methods of soldering, involving different fluxes, solders, and solder temperatures were used on five different can sizes and five
Design a factorial experiment whose three factors have 2, 3, and 4 levels, respectively. (a) List the factors and their levels. (b) Assuming that all interactions are to be included in the analysis of variance, what is the minimum number of replicates required for the degrees of freedom for error
Use statistical computer software to test for the significance of all estimated main effects and two- factor interactions at the 0.05 level of significance.
Estimate the values of any main effects found to be significant in Exercise 15.42.
State the conclusions of the experiment in words.
Show that for a = 2 the F test of a one- way analysis of variance is equivalent to the t test of Section 13.3 with d = 0 and the alternative hypothesis µ1 – µ2 ≠ 0.
Use Lagrange multipliers to show that the least squares estimates of the parameters of the model on page 425 are = .. and i = i – ...
Make use of the identityTo prove Theorem 15.3.
With reference to the notation on page 432, show that
For the two-way analysis of variance with a treatments and b blocks, show that
A random sample of size n = 2 is taken to test whether a normal population has the mean µ = 0.(a) If the observed sample values are x1 and x2 with x1 > x2 > 0, show that the statistic for the one-sample t-test can be written as(b) If the decimal point is erroneously moved one place to the
Show that if a one-way analysis of variance is per-formed on the ranks of the observations instead of the observations themselves, it becomes equivalent to a test based on the H statistic.
Verify the formula given on page 467 for the probability of getting u runs when u = 2k + 1, where k is a positive integer.
If a person gets seven heads and three tails in 10 tosses of a balanced coin, find the probabilities for 2, 3, 4, 5, 6, and 7 runs.
Find the probability that n1 = 6 letters of one kind and n2 = 5 letters of another kind will form at least 8 runs.
If there are n1 = 8 letters of one kind and n2 = 8 letters of another kind, for how many runs would we reject the null hypothesis of randomness at the 0.01 level of significance?
Given a set of k-tuples ( x11, x12, . . ., x1k), ( x21, x22, . . ., x2k), . . ., and ( xn1, xn2, . . ., xnk), the extent of their association, or agreement, may be measured by means of the coefficient of concordance:Where Ri is the sum of the ranks assigned to xi1, xi2, . . ., and xik when the
The following are the amounts of time, in minutes, that it took a random sample of 20 technicians to perform a certain task: 18.1, 20.3, 18.3, 15.6, 22.5, 16.8, 17.6, 16.9, 18.2, 17.0, 19.3, 16.5, 19.5, 18.6, 20.0, 18.8, 19.1, 17.5, 18.5, and 18.0. Assuming that this sample came from a sym-metrical
Rework Exercise 16.16 using the signed-rank test based on Table X.In exerciseThe following are the amounts of time, in minutes, that it took a random sample of 20 technicians to perform a certain task: 18.1, 20.3, 18.3, 15.6, 22.5, 16.8, 17.6, 16.9, 18.2, 17.0, 19.3, 16.5, 19.5, 18.6, 20.0, 18.8,
The following are the amounts of money (in dollars) spent by 16 persons at an amusement park: 20.15, 19.85, 23.75, 18.63, 21.09, 25.63, 16.65, 19.27, 18.80, 21.45, 20.29, 19.51, 23.80, 20.00, 17.48, and 19.11. Assuming that this is a random sample from a symmetrical population and that the
Rework Exercise 16.18 using the signed- rank test based on Table X. In exercise The following are the amounts of money (in dollars) spent by 16 persons at an amusement park: 20.15, 19.85, 23.75, 18.63, 21.09, 25.63, 16.65, 19.27, 18.80, 21.45, 20.29, 19.51, 23.80, 20.00, 17.48, and 19.11. Assuming
Show that under the null hypotheses of Section 16.3, T+ is a value of a random variable whose distribution is symmetrical about n(n + 1)/4 .
On what statistic do we base our decision and for what values of the statistic do we reject the null hypothesis if we have a random sample of size n = 10 and are using the signed- rank test at the 0.05 level of significance to test the null hypothesis µ = µ0 against the alternative hypothesis
Rework Exercise 16.20 with the level of significance changed to 0.01. In exercise On what statistic do we base our decision and for what values of the statistic do we reject the null hypothesis if we have a random sample of size n = 10 and are using the signed- rank test at the 0.05 level of
In a random sample taken at a public playground, it took 38, 43, 36, 29, 44, 28, 40, 50, 39, 47, and 33 minutes to play a set of tennis. Use the signed-rank test at the 0.05 level of significance to test whether it takes on the average 35 minutes to play a set of tennis at that public playground.
The following are figures on the numbers of burglaries committed in a city in random samples of six days in the spring and six days in the fall:Use the U test at the 0.01 level of significance to test the claim that on the average there are equally many burglaries per day in the spring as in the
The following are the Rockwell hardness numbers obtained for six aluminum die castings randomly selected from production lot A and eight from production lot B:Use the U test at the 0.05 level of significance to test whether the castings of production lot B are on the aver-age equally hard or
The following are the numbers of minutes it took random samples of 15 men and 12 women to complete a written test given for the renewal of their driver€™s licenses:Use the U test based on Table XI at the 0.05 level of significance to decide whether to accept the null hypothesis µ1 =
Rework Exercise 16.25 using the normal approximation to the distribution of the test statistic.In exerciseThe following are the numbers of minutes it took random samples of 15 men and 12 women to complete a written test given for the renewal of their driver€™s licenses:Use the U test
With reference to the data on page 460 and Example 16.6, calculate U as defined in Exercise 16.8 and verify that it equals the value obtained for U1.
The following is the order in which a broker received buy, B, and sell, S, orders for a certain stock: B B B B B B B B S S B S S S S S S B B B B B Test for randomness at the 0.05 level of significance.
With reference to the signed- rank test, find the mean and the variance of the random variable whose values are given by T+ – T–.
A driver buys gasoline either at a Texaco station, T, or at a Mobil station, M, and the following arrangement shows the order of the stations from which she bought gasoline over a certain period of time: T T T M T M T M M T T M T M T M T M M T M T Test for randomness at the 0.05 level of
The following is the order in which red, R, and black, B, cards were dealt to a bridge player: B B B R R R R R B B R R R Test for randomness at the 0.05 level of significance.
The following arrangement indicates whether 60 consecutive cars that went by the toll booth of a bridge had local plates, L, or out- of- state plates, O:L L O L L L L O O L L L L O L O O L L L L O L O O L L L L L O L L L O L O L L L L O O L O O O O L L L L O L O O L L L OTest at the 0.05 level of
To test whether a radio signal contains a message or constitutes random noise, an interval of time is sub-divided into a number of very short intervals, and for each of these it is determined whether the signal strength exceeds, E, or does not exceed, N, a certain level of background noise. Test at
The following are the numbers of students absent from school on 24 consecutive school days: 29, 25, 31, 28, 30, 28, 33, 31, 35, 29, 31, 33, 35, 28, 36, 30, 33, 26, 30, 28, 32, 31, 38, and 27. Test for randomness at the 0.01 level of significance.
The following are six years’ quarterly sales (in millions of dollars) of a manufacturer of heavy machinery: 83.8, 102.5, 121.0, 90.5, 106.6, 104.8, 114.7, 93.6, 98.9, 96.9, 122.6, 85.6, 103.2, 96.9, 118.0, 92.1, 100.5, 92.9, 125.6, 79.2, 110.8, 95.1, 125.6, and 86.7. At the 0.05 level of
The theory of runs may also be used as an alternative to the rank- sum test of Section 16.4, that is, the test of the null hypothesis that two independent random samples come from identical continuous populations. We simply rank the data jointly, write a 1 below each value belonging to the first
Calculate rS for the following data representing the statistics grades, x, and psychology grades, y, of 18 students:
With reference to Exercise 16.38, test at the 0.05 level of significance whether the value obtained for rS is significant.In exercise
Explain why, among others, there is a blank in Table X for n = 5 in the column for T0.02.
Calculate rS for the data of Exercise 14.40 and test the null hypothesis of no correlation at the 0.05 level of significance.In exercise

Showing 40100 - 40200 of 88243

First
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
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