Introductory Probability And Statistical Applications 2nd Edition Paul L. Meyer - Solutions

Unlock the potential of your learning experience with the "Introductory Probability And Statistical Applications 2nd Edition" by Paul L. Meyer. Discover a comprehensive collection of solved problems and step-by-step answers with our online solutions. Our answers key and solution manual provide detailed chapter solutions to enhance your understanding. Access the instructor manual and test bank for an in-depth study approach. Whether you're looking for textbook solutions or a free download of the solutions PDF, we have all your questions and answers covered. Embrace success with our expertly crafted online resources tailored for every learner!

Which of followings is a dummy variable?a. Age (18 to 64 years of age)b. Five- point Likert scale (1 to 5)c. Depression scores (0 to 60)d. Religion (0 to 1)
These value categories can be used in SPSS except:a. (1 = Male, 2 = Female)b. (Y = Yes, N = No)c. (1 = Democrat, 2 = Republican, 3 = Other)d. N one of the above
Which of the followings can be used as a SPSS variable name?a. Annual Incomeb. Annual- Incomec. Annual.Incomed. AnnualIncome
In your own judgment, what are the strengths and limitations of this study and what could be done differently?Review a current empirical- research- based article in a professional social science/ health care journal in your area of interest and answer the following questions. Attach the article
Discuss the relationships among the dependent and independent variables and their directions.Review a current empirical- research- based article in a professional social science/ health care journal in your area of interest and answer the following questions. Attach the article along with your
W hat type of statistical methods (descriptive or inferential) were used to analyze the data?
Discuss the reliability and validity of the instrument(s).Review a current empirical- research- based article in a professional social science/ health care journal in your area of interest and answer the following questions. Attach the article along with your answers.
W hich instrument(s) were used to measure the dependent variable(s)?Review a current empirical- research- based article in a professional social science/ health care journal in your area of interest and answer the following questions. Attach the article along with your answers.
W hat are the independent and dependent variables under study and their levels of measurement?Review a current empirical- research- based article in a professional social science/ health care journal in your area of interest and answer the following questions. Attach the article along with your
W hat are the null and alternative hypotheses?Review a current empirical- research- based article in a professional social science/ health care journal in your area of interest and answer the following questions. Attach the article along with your answers.
Briefly summarize the article’s main purpose, methods, and major findings.Review a current empirical- research- based article in a professional social science/ health care journal in your area of interest and answer the following questions. Attach the article along with your answers.
In a study involving refugees with a limited English vocabulary, participants consistently recorded the word “cup” when they heard the word “cop.” This is an example of a ________________.
In question 17, the dependent variable is ________________ and the independent variable is ________________ .
The statement, “Participants in the experimental group will significantly improve their levels of self- worth compared to participants in the control group,” is an example of a(an) ________________.
If a test is highly correlated with another test measuring the same construct under study, this would be an example of ________________.
A measure is said to have ________________ if it appears to measure what it intended to measure.
A measure that indicates on a 7- point scale how severe a mental health patient experienced anxiety attack would be a(n) ________________ level of measurement.
In question 12, the independent variable is ________________ and the dependent variable is ________________.
If the results of a study show that students who exercised regularly decreased their body mass index (BMI), then this is an example of ________________.
Dr. Jones administered the same instrument to the same subjects in two different occasions.She is thus seeking to evaluate the ________________ of the instrument.
If a measure is valid with one culture, it must also be valid in another culture.a. Trueb. False
The sum of the square of X values is equal to the square of the sum of these X values.a. Trueb. False
A research hypothesis will always predict a significant relationship between two variables.a. Trueb. False
If a measure is said to predict a future outcome, then it has a good test– retest reliability coefficient.a. Trueb. False
Dr. Nagham found a significant relationship between life satisfaction and depressive symptoms among a sample of 100 older adults. However, after conducting further statistical analysis, Dr. Nagham concluded that the relationship between these two variables was due to participants’ levels of
These are types of measurement’s psychometric properties except:a. C onstruct validityb. E quivalence coefficientc. C orrelation coefficientd. Stability coefficient
W hich of the following is an example of an interval level of measurement?a. Major in graduate schoolb. Time required to complete a statistics quizc. An intelligence testd. N umber of police citations in the last year
Marital status, political party affiliation, and hair color all are examples of what level of measurement?a. Nominalb. Ordinalc. Intervald. Ratio
Dr. Bader was interested in the number of migraine headaches his clients experienced in the past month. Number of headaches is thus measured at what level of measurement?a. Nominalb. Ordinalc. Intervald. Ratio
W hich of the following are variables?a. Dentist, teacher, pilotb. Male, divorce, Native Americanc. Occupation, education, ethnicityd. N one of the above
15.12. Suppose that the random variable X has the following pdf: a cos ax f(x) = 0 < x 1. (a) Obtain an expression for the OC function of this test, say L(a), and graph it. (b) What is the size of this test if ao = */4?
15.11. In using various failure laws we have found that the exponential distribution plays a particularly important role, and hence it is important to be able to decide whether a particular sample of failure times comes from an underlying exponential distribution. Suppose that 335 light bulbs have
15.10. Three kinds of lubricants are being prepared by a new process. Each lubricant is tested on a number of machines, and the result is then classified as acceptable or non- acceptable. The data in Table 15.1 represent the outcome of such an experiment. Test the hypothesis that the probability p
15.9. (a) Compute the expected value of the random variable D as defined in Eq. (15.4). (b) How does this value compare with the (asymptotic) expected value of D obtained from the chi-square distribution which may be used to approximate the distribution of D2 when n is large?
15.8. If n = 4 and k = 3, how many possible values may the random variable D, as defined in Eq. (15.4), assume?
15.7. It is known that a large shipment of volt meters contains a certain proportion of defectives, say p. To test Ho: p = 0.2 versus H: p > 0.2, the following procedure is used. A sample of size 5 is obtained and X, the number of defective voltmeters, is counted. If X1, accept Ho; if X> 4, reject
15.6. Verify the properties for the OC function R(p) as defined in Eq. (15.3).
15.5. Verify the properties for the OC function L(p) as defined in Eq. (15.2).
15.4. Establish Properties of Eq. (15.1) for the OC function L(u) = [(C - )n/o].
15.3. Suppose that X has a Poisson distribution with parameter A. To test Ho: = Ao versus H: A > Ao, the following test is proposed. Obtain a sample of size n, compute the sample mean X, and reject Ho whenever > C, where C is a constant to be determined. (a) Obtain an expression for the OC function
15.2. Consider the situation described in Problem 15.1 except that the alternative hypothesis is of the form H: o. Hence we reject Ho whenever X-40 > C. Answer questions (a) and (b) above.
15.1. Suppose that X has distribution N(u, 2) with 2 known. To test o: = 10 versus H:
14.37 With the aid of Table 7, obtain a sample of size 20 from a random variable having N(2, 4) distribution. (a) Suppose that this sample was obtained from a random variable having distribution N(a, 4). Use the sample values to obtain a 95 percent confidence interval fora. (b) Same as (a) except
14.36. Suppose that E(Y) = ax2 + 8X + %, where X is preassigned. Based on a sample (x, y), i = 1,..., n, determine the least squares estimates of the parametersa, , and Y.
14.35. Verify the expressions for (a) and (B) as given by Eq. (14.9).
14.34. Verify that the least squares estimates & and as given by Eqs. (14.7) and (14.8) are unbiased.
14.33. It might be (erroneously) supposed that an unbiased estimate may always be found for an unknown parameter. That this is not so is illustrated by the following example. Suppose that n repetitions of an experiment are made and a particular event A occurs precisely k times. If there is
14.32. Suppose that E(Y) aX+8. A sample of size 50 is available, say (xi, Y.), 15 and x;; = 8. i = 1,..., 50 for which x = Y = 0, x = 10, (a) Determine the least squares estimates of the parameters a and , say & and B. (b) What is the value of the minimum sum of squares [Y; (ax + B)].
14.31. The following sample of size 5 was obtained from the two-dimensional ran- dom variable (X, Y). Using these values, compute the sample correlation coefficient. x 1 2 3 4 5 y 4 5 3 1 2
14.30. Suppose that X is normally distributed. A random sample of size 4 is obtained and the sample mean is computed. If the sum of the squares of the deviations of these 4 measurements from X equals 48, obtain a 95 percent (two-sided) confidence interval for E(X) in terms of X.
14.29. Suppose that the random variable has Student's 1-distribution with 1 degree of freedom. What is the distribution of t? Identify it.
14.28. One reason for the importance of the F-distribution is the following. Suppose that X and Y are independent random variables with distributions N(, ) and N(y, o), respectively. Let X1, ..., X and Y,..., Yn, be random samples from X and Y, respectively. Then the statistic C (XX)/E (YY)2 has an
14.27. Sketch the graph of the pdf h as given in Problem 14.26, assuming that n > n2 > 2.
14.26. (The F-distribution.) Let X and Y be independent random variables having X, and x, distributions, respectively. Let the random variable F be defined as follows: F = (X/n)/(Y/n) = n2X/nY. (This random variable plays an important role in many statistical applications.) Show that the pdf of F
14.25. Suppose that X, the length of a bolt, has distribution N(, 1). A large number of bolts are manufactured and subsequently separated into two large stockpiles. Stock- pile 1 contains only those bolts for which X > 5, while stockpile 2 contains all the re- maining bolts. A sample of size n is
14.24. One hundred components were tested, and 93 of these functioned more than 500 hours. Obtain a (two-sided) 95-percent confidence interval for p P (component functions more than 500 hours). [Hint: Use Eq. 14.12.]
14.23. Suppose that X has distribution N(u, 2), where and 2 are unknown. A sample of size 15 has yielded the values X = 8.7 and X=27.3. Obtain a (two-sided) 95-percent confidence interval for o. =>
14.22. Obtain a one-sided (lower) 99-percent confidence interval for R(100) of Prob- lem 14.21.
14.21. Suppose that the life length of a component is normally distributed, say N(, 9). Twenty components are tested and their time to failure X1,..., X20 is recorded. Suppose that 100.9 hours. Obtain a 99-percent (two-sided) confidence interval for the reliability R(100).
14.20. Suppose that X has distribution N(, 4). A sample of size 25 yields a sample mean =78.3. Obtain a 99-percent (two-sided) confidence interval for .
14.19. Suppose that X has distribution N(u, 2). A sample of size 30, say x1,..., X30, yields the following values: 1 X = 700.8, 1X = 16,395.8. Obtain a 95- percent (two-sided) confidence interval for .. =1
14.18. Compare the value of P(X1), where X has distribution N(0, 1), with P(1), where 7 has Student's 1-distribution with: (a) 5 df (b) 10 df (c) 15 df (d) 20 df (e) 25 df 30
14.17. Prove Theorem 14.3. [Hint: See Note (a) following this theorem.]
14.16. Suppose that X has a Weibull distribution with pdf f(x)=(a)x-le- x > 0. Suppose that a is known. Find the ML estimate of X based on a sample of size n.
14.15. Suppose that X has a Gamma distribution; that is, the pdf is given by f(x) A(x) T(r) x > 0. Suppose that r is known. Let X,..., X, be a sample of X and obtain the ML estimate of based on this sample.
14.14. A random variable X has distribution N(, 1). Twenty observations are taken on X but instead of recording the actual value we only note whether or not X was nega- tive. Suppose that the event {X < 0) occurred precisely 14 times. Using this informa- tion, obtain the ML estimate of .
14.13. Let us assume that a-particles are emitted from a radioactive source according to a Poisson distribution. That is, if X is the number of particles emitted during an inter- val of 1 minutes, then P(X = k) = e^(A)/k! Instead of recording the actual number of particles emitted, suppose that we
14.11 are used in (a) a series connection, and (b) a parallel connection. In each case find the ML estimate of the reliability for a 1600-hour operation of the system, based on the sample values given in Problem 14.11.
14.12. Suppose that two lamps as described in Problem
14.11. The following data represent the life length of electric lamps (in hours): 1009, 1085, 1123, 1181, 1235, 1249, 1263, 1292, 1327, 1338, 1348, 1352, 1359, 1368, 1379, 1397, 1406, 1425, 1437, 1438, 1441, 1458, 1483, 1488, 1499, 1505, 1509, 1519, 1541, 1543, 1548, 1549, 1610, 1620, 1625, 1638,
14.10. A component assumed to have an exponential failure distribution was tested. The following life lengths (in hours) were observed: 108, 212, 174, 130, 198, 169, 252, 168, 143. Using these sample values, obtain the ML estimate for the reliability of the com- ponent when used for a period of 150
14.9. (a) A procedure is performed until a particular event A occurs for the first time. On each repetition P(A) = p. Suppose that n repetitions are required. Then this ex- periment is repeated, and this time n2 repetitions are required to yield the event A. If this is done k times, we obtain the
14.8. Suppose that X is uniformly distributed over (-a, a). Find the ML estimate of a based on a random sample of size n, X1, ..., X.
14.7. Consider the same failure law as described in Problem 14.6. This time N items are tested for To hours (To > fo), and the number of items that fail in that period is recorded, say k. Answer question (a) of Problem 14.6.
14.6. Suppose that T, the time to failure (in hours) of an electronic device, has the following pdf: f(1) = Be-Bit-to), t> to > 0, = = 0, elsewhere. (T has an exponential distribution truncated to the left at 10.) Suppose that n items are tested and the failure times T,..., T, are recorded. (a)
14.5. The data in Table 14.4 were obtained on the distribution of depth of sapwood in telephone poles. (W. A. Shewhart, Economic Control of Quality of Manufactured Products. Macmillan and Co., New York, 1932, p. 66.) Assuming that the random variable under consideration has distribution N(u, 2),
14.4. A random variable X has pdf f(x) = (8 + 1)x, 0 < x < 1. (a) Obtain the ML estimate of , based on a sample X1, ..., X. (b) Evaluate the estimate if the sample values are 0.3, 0.8, 0.27, 0.35, 0.62, and 0.55.
14.3. Suppose that 200 independent observations X1, ..., X200 are obtained from a random variable X. We are told that 200X300 and that Using these values, obtain an unbiased estimate for E(X) and V(X).
14.2. Let X be a random variable with expectation and variance o. Let (X1, ..., X,) be a sample of X. There are many other estimates of o2 which suggest themselves in addition to the one proposed earlier. Show that C (X+1X) is an unbiased estimate of o for an appropriate choice of C. Find that
14.1. Suppose that an object is measured independently with two different measuring devices. Let L1 and L2 be the measured lengths obtained from the first and second device, respectively. If both devices are calibrated correctly we may assume that E(L1) = E(L2) =L, the true length. However, the
13.15 Let X have distribution N(0, 1). Let X1, ..., X30 be a random sample of X obtained by using Table 7. Compute P(X2 0.10) and compare this value with the relative frequency of that event.Depth of Sapwood (in.) Frequency Depth of Sapwood (in.) Frequency 1.9 9399 1.0 2 1.3 29 3.7 4.0 123 82 1.6
13.14 Suppose that X has distribution N(2, 9). Let X1, ..., X20 be a random sample of X obtained with the aid of Table 7. Compute 1 (x - 72 n-1 i=1 and compare it with E(S) = 9.
13.13 Let X have distribution N(0, 1). From Table 7 in the appendix, obtain a sample of size 20 from this distribution. Let Y = |X]. (a) Use this sample to compare P[1 < Y
13.12. (For this exercise and the following three, read the Note at the end of Chapter 13.) Use the table of normal deviates (Table 7, appendix) and obtain a sample of size 30 from a random variable X having a N(1, 4) distribution. Use this sample to answer the following: (a) Compare P(X 2) with
13.11. Independent samples of size 10 and 15 are taken from a normally distributed random variable with expectation 20 and variance 3. What is the probability that the means of the two samples differ (in absolute value) by more than 0.3?
13.10. A continuous random variable X is uniformly distributed over (-). A sample of size n is obtained from X and the sample mean X is computed. What is the standard deviation of X?
13.9. Using the scheme outlined in Problem 13.8, obtain a random sample of size 3 from the distribution X.
13.8. In Section 13.5 we have indicated a method by which random samples from a specified distribution may be generated. There are numerous other methods by which this may be done, some of which are to be preferred to the one given, particularly if com- puting devices are available. The following
13.7. Using a table of random numbers, obtain a random sample of size 8 from a random variable having the following distributions: (a) exponential, with parameter 2, (b) chi-square with 7 degrees of freedom, (c) N(4, 4).
13.6. Suppose that X has distribution N(0, 0.09). A sample of size 25 is obtained from X, say X1,..., X25. What is the probability that , X exceeds 1.5?
13.5. The life length (in hours) of an item is exponentially distributed with parameter 8 = 0.001. Six items are tested and their times to failure recorded. (a) What is the probability that no item fails before 800 hours have elapsed? (b) What is the probability that no item lasts more than 3000
13.4. A sample of size 5 is obtained from a random variable with distribution N(12,4). (a) What is the probability that the sample mean exceeds 13?(b) What is the probability that the minimum of the sample is less than 10? (c) What is the probability that the maximum of the sample exceeds 15?
13.3. Suppose that X has a geometric distribution with parameter p. Let X1,..., Xn be a random sample from Xand let M = max (X1,..., X) and K = min (X1,..., Xn). Find the probability distribution of M and of K. [Hint: P(Mm) = F(m) - F(m - 1), where F is the cdf of M.]
13.2. Show that if X1, ..., X, are independent random variables, each having an ex- ponential distribution with parametera, i = 1, 2,...,n, and if K min (X1,..., Xn), then K has an exponential distribution with parameter a ++an. (See Theorem 13.3.)
13.1. Derive the expression for the pdf of the minimum of a sample. (See Theorem 13.2.)
12.13. Suppose a new apparatus is tested repeatedly under certain stress conditions until it fails. The probability of failure on any trial is p1. Let X be equal to the number of trials required up to and including the first failure. A second apparatus is also tested repeatedly until it fails.
12.12. (a) An electronic device has failure time 7 whose distribution is given by N(100, 4). Suppose that in recording 7 an error is made whose value may be represented as a random variable X, uniformly distributed over (-1, 1). If X and T are independent, obtain the pdf of S = X + T in terms of +,
12.11. Perform the calculations suggested at the end of Example 12.5.
12.10. Suppose that X and Y are independent, identically distributed random vari- ables. Assume that the pdf of X (and hence of Y) is given by f(x) = a/x, x >a, a > 0, = 0, elsewhere.
12.9. In measuring 7, the life length of an item, an error may be made which may be assumed to be uniformly distributed over (-0.01, 0.01). Thus the recorded time (in hours) may be represented as 7+ X, where 7 has an exponential distribution with parameter 0.2 and X has the above-described uniform

Showing 400 - 500 of 4976

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Last

Introductory Probability And Statistical Applications 2nd Edition Paul L. Meyer - Solutions

Step by Step Answers