Mathematical Statistics with Applications
7th Edition
ISBN: 9780495110811
Author: Dennis Wackerly, William Mendenhall, Richard L. Scheaffer
Publisher: Cengage Learning
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Chapter 11.4, Problem 17E
a.
To determine
Find the values of SSE and
b.
To determine
Fit the model
Find the value of
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People having Raynauds syndrome are apt to suffer a sudden impairment of blood circulation in fingers and toes. In an experiment to study the extent of this impairment, each subject immersed a forefinger in water and the resulting heat output (cal/cm2/min) was measured. For m = 12 subjects with the syndrome, the average heat output was x = 0.64, and for n = 12 non-sufferers, the average output was 2.05. Let µ1 and µ2 denote the true average heat outputs for the two types of subjects. Assume that the two distributions of heat output are normal with σ1 = 0.2 and σ2 = 0.2.
1) Consider testing H0: µ1 − µ2 = 0 versus Ha: µ1 − µ2 < 0 at level 0.01. Describe in words what Ha says, and then carry out the test.
2) What is the probability of a type II error when the actual difference between µ1 and µ2 is µ1 − µ2 = −1.2?
3) Assuming that m=n, what sample sizes are required to ensure that β=0.1when µ1− µ2 = −1.2?
For a population with µ = 40 and σ = 8, what is the X value corresponding to z = 1.50?
Suppose that h(x) is the hazard function of X, and h(x)=?λ for all x.
(a) Calculate the survival function S(x).
(b) Derive the mean life E(X) and the mean residual life E(X-x|X>x), where E(X) is a special case of mean residual life with x=0.
(c) Based on your answer in (b), do you think h(x) can be used to model human lifespan?
answer a, b, and c
Chapter 11 Solutions
Mathematical Statistics with Applications
Ch. 11.3 - If 0 and 1 are the least-squares estimates for the...Ch. 11.3 - Prob. 2ECh. 11.3 - Fit a straight line to the five data points in the...Ch. 11.3 - Auditors are often required to compare the audited...Ch. 11.3 - Prob. 5ECh. 11.3 - Applet Exercise Refer to Exercises 11.2 and 11.5....Ch. 11.3 - Prob. 7ECh. 11.3 - Laboratory experiments designed to measure LC50...Ch. 11.3 - Prob. 9ECh. 11.3 - Suppose that we have postulated the model...
Ch. 11.3 - Some data obtained by C.E. Marcellari on the...Ch. 11.3 - Processors usually preserve cucumbers by...Ch. 11.3 - J. H. Matis and T. E. Wehrly report the following...Ch. 11.4 - a Derive the following identity:...Ch. 11.4 - An experiment was conducted to observe the effect...Ch. 11.4 - Prob. 17ECh. 11.4 - Prob. 18ECh. 11.4 - A study was conducted to determine the effects of...Ch. 11.4 - Suppose that Y1, Y2,,Yn are independent normal...Ch. 11.4 - Under the assumptions of Exercise 11.20, find...Ch. 11.4 - Prob. 22ECh. 11.5 - Use the properties of the least-squares estimators...Ch. 11.5 - Do the data in Exercise 11.19 present sufficient...Ch. 11.5 - Use the properties of the least-squares estimators...Ch. 11.5 - Let Y1, Y2, . . . , Yn be as given in Exercise...Ch. 11.5 - Prob. 30ECh. 11.5 - Using a chemical procedure called differential...Ch. 11.5 - Prob. 32ECh. 11.5 - Prob. 33ECh. 11.5 - Prob. 34ECh. 11.6 - For the simple linear regression model Y = 0 + 1x...Ch. 11.6 - Prob. 36ECh. 11.6 - Using the model fit to the data of Exercise 11.8,...Ch. 11.6 - Refer to Exercise 11.3. Find a 90% confidence...Ch. 11.6 - Refer to Exercise 11.16. Find a 95% confidence...Ch. 11.6 - Refer to Exercise 11.14. Find a 90% confidence...Ch. 11.6 - Prob. 41ECh. 11.7 - Suppose that the model Y=0+1+ is fit to the n data...Ch. 11.7 - Prob. 43ECh. 11.7 - Prob. 44ECh. 11.7 - Prob. 45ECh. 11.7 - Refer to Exercise 11.16. Find a 95% prediction...Ch. 11.7 - Refer to Exercise 11.14. Find a 95% prediction...Ch. 11.8 - The accompanying table gives the peak power load...Ch. 11.8 - Prob. 49ECh. 11.8 - Prob. 50ECh. 11.8 - Prob. 51ECh. 11.8 - Prob. 52ECh. 11.8 - Prob. 54ECh. 11.8 - Prob. 55ECh. 11.8 - Prob. 57ECh. 11.8 - Prob. 58ECh. 11.8 - Prob. 59ECh. 11.8 - Prob. 60ECh. 11.9 - Refer to Example 11.10. Find a 90% prediction...Ch. 11.9 - Prob. 62ECh. 11.9 - Prob. 63ECh. 11.9 - Prob. 64ECh. 11.9 - Prob. 65ECh. 11.10 - Refer to Exercise 11.3. Fit the model suggested...Ch. 11.10 - Prob. 67ECh. 11.10 - Fit the quadratic model Y=0+1x+2x2+ to the data...Ch. 11.10 - The manufacturer of Lexus automobiles has steadily...Ch. 11.10 - a Calculate SSE and S2 for Exercise 11.4. Use the...Ch. 11.12 - Consider the general linear model...Ch. 11.12 - Prob. 72ECh. 11.12 - Prob. 73ECh. 11.12 - An experiment was conducted to investigate the...Ch. 11.12 - Prob. 75ECh. 11.12 - The results that follow were obtained from an...Ch. 11.13 - Prob. 77ECh. 11.13 - Prob. 78ECh. 11.13 - Prob. 79ECh. 11.14 - Prob. 80ECh. 11.14 - Prob. 81ECh. 11.14 - Prob. 82ECh. 11.14 - Prob. 83ECh. 11.14 - Prob. 84ECh. 11.14 - Prob. 85ECh. 11.14 - Prob. 86ECh. 11.14 - Prob. 87ECh. 11.14 - Prob. 88ECh. 11.14 - Refer to the three models given in Exercise 11.88....Ch. 11.14 - Prob. 90ECh. 11.14 - Prob. 91ECh. 11.14 - Prob. 92ECh. 11.14 - Prob. 93ECh. 11.14 - Prob. 94ECh. 11 - At temperatures approaching absolute zero (273C),...Ch. 11 - A study was conducted to determine whether a...Ch. 11 - Prob. 97SECh. 11 - Prob. 98SECh. 11 - Prob. 99SECh. 11 - Prob. 100SECh. 11 - Prob. 102SECh. 11 - Prob. 103SECh. 11 - An experiment was conducted to determine the...Ch. 11 - Prob. 105SECh. 11 - Prob. 106SECh. 11 - Prob. 107SE
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- Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.arrow_forwardA sample of n =16 scores produces a t statistic of t = 2.00. If the sample is used to measure effect size with r2, what value will be obtained for r2arrow_forwardA researcher hypothesizes that in a certain country the net annual growth of private sector purchases of government bonds, B, is positively related to the nominal rate of interest on the bonds, NI, and negatively related to the rate of inflation Π: Bt = a0 + a1NIt + a2Π t + ut Note that it may be hypothesized that B depends on the real rate of interest on bonds, R, where R = NI – Π. Using a sample of 56 annual observations, s/he estimates the following equations: (1) Bt = 0.43 + 0.90NIt - 0.97Πt R21 = 0.962, SSR1 = 2.20, QRESET(F1,52) = 16.6 (3.58) (8.80) (-1.05) (2) Bt = 0.44 + 0.94Rt R22 = 0.960, SSR2 = 2.22, QRESET(F1,53) = 0.9 (9.70) (16.7) (3) Bt = 0.44 + 1.14NIt SSR3 = 9.20, QRESET(F1,53) = 59.9 (8.84) (36.1) (4) NIt = 0.08 + 0.94Πt R24 = 0.997, SSR4 = 0.18, QRESET(F1,53) = 1.4…arrow_forward
- You have received a radioactive mass that is claimed to have a mean decay rate of at least 1 particle per second. If the mean decay rate is less than 1 per second, you may return the product for a refund. Let X be the number of decay events counted in 10 seconds. a) If the mean decay rate is exactly 1 per second (so that the claim is true, but just barely), what is P(X ≤ 1)? b) Based on the answer to part (a), if the mean decay rate is 1 particle per second, would one event in 10 seconds be an unusually small number? c) If you counted one decay event in 10 seconds, would this be convincing evidence that the product should be returned? Explain. d) If the mean decay rate is exactly 1 per second, what is P(X ≤ 8)? e) Based on the answer to part (d), if the mean decay rate is 1 particle per second, would eight events in 10 seconds be an unusually small number? f) If you counted eight decay events in 10 seconds, would this be convincing evidence that the product should be returned? Explain.arrow_forwardA regression on the original regressors, ?̂t2 and a constant term yields the following statistics: R2 = 0.296041 F = 1.177507 coeff of ?̂t2 has a t-statistic of 2.876 With this information, which test can you implement to deal with the problem omitted variables and why? Implement the test as stated in b(i) and interpret the results. What is (are) the consequence(s) of the problem alluded to above on the estimators?arrow_forwardAn experiment was conducted to see the effectiveness of two antidotes to three different doses of a toxin. The antidote was given to a different sample of participants five minutes after the toxin. Thirty minutes later the response was measured as the concentration in the blood. What can the researchers conclude with α = 0.05? Dose Antidote 5 10 15 1 0.61.11.1 7.21.52.4 3.14.15.9 2 1.11.21.1 1.71.31.5 2.13.12.1 A) Obtain/compute the appropriate values to make a decision about H0.Antidote: critical value = test statistic = Decision: Dose: critical value = test statistic = Decision: Interaction: critical value = test statistic = Decision: B) Compute the corresponding effect size(s) and indicate magnitude(s).Antidote: η2 = Dose: η2 = Interaction: η2 =arrow_forward
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